Here are my criticisms of your cards. I apologize in advance if I'm too harsh. There are very few fan cards that I like.
Sorcerer's Apprentice
+1 Action
Reveal the top card of your deck. Choose 1:
Put it back, discard it, put it into your hand, trash it.
--
If you reveal this from the top of your deck, you may put this into your hand. If you do, if it is your turn, +1 Action; and continue to reveal cards as if you handn't revealed this card.
Action-reaction
$2
Two parts of this card rub me the wrong way: "If you do, if it is your turn, +1 Action" and "continue to reveal cards as if you handn't revealed this card." It would be nice if the entire benefit gained from revealing the card was available whether or not it was your turn. Why +1 Action anyway? Sorcerer's Apprentice is already non-terminal. Honestly, I think putting the card into your hand is enough of a bonus. That being said, there is bound to be some wackiness for an effect that triggers on being revealed from your deck. If I recall correctly, Donald tried it at one point and rejected it for being too confusing. I might be misremembering the specifics.
Also, it shouldn't be a Reaction card. You're already revealing it and the events trigger from that. Reactions are for when the card isn't already public knowledge and you get to reveal/discard/trash it at a time when you wouldn't normally be able to do so.
Satyr
Choose one: +2 cards; +2 actions; +$2; or +2 buys
Action
$2
I think this one might need to be buffed up, but who knows?
This card just isn't interesting to me. The card concept seems to be: a cheap card that gives you a choice between several weak effects. We've got plenty of that already (Pawn, Steward, Squire, etc.). If you're creating a new card for that concept, it has to be pretty interesting (like Squire).
However, the problem you run into there is that if you give four complex options, the card becomes a confusing, bloated mess. Case in point:
Sphinx
Choose one: +3 cards, put a card from your hand on top of your deck; +3 actions, all other action cards played this turn do not give you +actions; +$3, All treasure (except Copper, maybe?) are worth 1 less; or trash three cards from your hand, gain a card costing up to 4
Action
$3
I'd cut this down to 2 or 3 options. The first one I'd cut is the +3 Actions, since "all other Action cards played this turn do not give you +Actions" just seems kludgy and weird to me. Also, rinkworks is right: if you keep the "All Treasure cards produce $1 less this turn (but not less than $0)" bit, you can't exclude Copper without making Sphinx-BM the dominant strategy in every Sphinx game.
Basement
(+ 1 Action)
Reveal then discard any number of cards. +2 card per Treasure card discarded in this way, +1 card per other card discarded this way. You may trash this card.
--
When you trash this card, +1 card.
Action
$3
I'm very worried that this is also going to promote boring strategies by making you want only Treasures and Basements in your deck. I do like the fact that you can trash the card and it has an on-trash ability.
Wealthy Village
If played as an action;
+1 card, +2 actions
--
If played as a treasure;
$2
Action-Treasure
$4
In general, you can't charge $4 for a Silver+. There are lots of times where you'll happily buy a Silver for $4 and when Wealthy Villages are available you'll just buy them instead. It has to cost at least $5.
I'm against Action-Treasure cards in general. I don't think the novelty is worth the potential confusion. But that's just my opinion.
Villager
+1 card
+2 actions
Look at the top and bottom card of your deck. Discard one and put the other on top of your deck.
Action
$4
This card doesn't seem like a standout to me, but as deck lubricant goes it's solid. Two thumbs up.
Pegasus
+1 card
+1 action
You may reveal and discard an Action or Treasure card. If it is an Action card, +1 buy, +$1. If it is a Treasure card, +1 Card, +1 Action
Action
$4
First of all, if you're discarding a single card, you don't need to explicitly reveal it; the card is already public knowledge (e.g. Jester). It's only when you're discarding 2 or more cards at once when you need reveal them first (e.g. Tribute). Second, why limit the discard to an Action or Treasure? You don't get a bonus for discarding anything else anyway, so why not let it happen? Third, the bonus for discarding an Action card is way, way too weak. Pegasus gives you a +1 Action. You could have played that Action card! The bonus should be way stronger than +1 Buy and +$1. Finally, I think the card would be interesting if the discard was mandatory.
Sorcerer
+1 card
+1 action
At the start of your next turn, +$1
--
While this is in play, whenever someone buys a victory card, +$1 more on your next turn. This cannot cause you to get more than +$3 on your next turn.
Action-Duration
$4
The core idea of this card seems to be: get a bonus for things your opponents do during their turns. I think the idea is fine. It would be nice if the bonus were easier to track and didn't have a hard limit. Something like, "You may discard a card. If you do, +1 Card."
Centaur
+$2
Each other player gains a copy of the top card of the Centaur pile, then put the top card of the Centaur pile on the bottom.
--
Set up: Shuffle together the Copper, Curse, and Estate randomizer cards and place them face up on the board. This is the Centaur pile.
Action-Attack
$4
I think this is probably fine, if a bit swingy. It's probably no swingier than Swinder. I don't think that the newer copies of Dominion have randomizers for Copper, Estate, and Curse, but they could be easily proxied with blanks.
Before moving on with the individual card critiques, I'd like to step back and take a more holistic look at the set. I find that the set lacks exciting cards that really jump out at me. I think one reason is that a lot of the cards are just too vanilla. By that I mean that most of their effect is a combination of (or a choice between) very basic components (+Cards, +Actions, etc.).
I think the biggest problem, though, is that you seem to suffer from extreme Non-Terminalitis. (Don't worry, it's not terminal!
) Looking through the 14 Action cards in your set, Centaur is the
only one that you're not at least considering giving +Actions to.
In general, most cool cards with flashy effects are balanced, at least in part, by being terminal Actions. +1 Action is a very powerful thing for a card to have, and if you have to balance the card around it, the rest of the card has to be less powerful. That may not be the best way to think about it, but it's something to keep in mind. Your set should have some non-terminal Actions, of course. Every set needs some deck lubricant cards, like Hamlet, Oasis, Vagrant, Ironmonger, Cellar, etc. But when most of your set is deck lubricant, something is wrong.
Luckily, it's not all that tough to determine which cards should be non-terminal. Some cards need to be non-terminal in order to fit their concept. Time Machine, for instance, makes sense as a non-terminal so that you're encouraged to gain a cool Action card into your hand rather than a basic Treasure card. Village cards are non-terminal by nature and every set should have some of those.
I'll pick on two other examples from your set. The whole point of Dragon's Hoard is that it's the only Action card you play that turn. Why in the world is it non-terminal? I mean, I think I can see your thought process. If a player draws it with another Action card you want them to still be able to use it as a pseudo-Copper. Resist! Oftentimes a card with some risk involved is better than a risk-free card. A less obvious example is Sorceror. All Sorceror really needs is an effect next turn and its whlie-in-play effect. It'll probably end up having a this-turn effect too, but there's no reason that it needs to include +1 Action.
Time Machine
+1 action
Gain a copy of an action card that the player to your right played of their last turn and put it into your hand.
Action
$5
I like the idea, but it's hard to implement well. The first problem that jumped out at me when I read the card is that if your right-hand opponent played a Time Machine, you can play your Time Machine to gain a Time Machine into your hand. Then you can play that Time Machine to gain a Time Machine into your hand, etc.
Furthermore, I think it'll lead to people playing Action-less strategies in order to deny their left-hand opponents the awesome benefits this card provides. Again, I like the idea, but I assume the gain-into-hand is an essential part of the card, and I'm not sure how you could make that work.
Dragon's Hoard
+$1, +1 action
During your Buy phase, if this is your only action card in play, +$2, +1 buy
Action
$5
This is another card that I think will promote boring Treasure-centric strategies.
Cursed Treasury
+1 Card
+1 Action
+1 Buy
You may gain a Curse card. If you do,
+1 Card
+$2
Action
$5
Too vanilla for my taste. Sorry.
Area 51
+1 card
+1 action
Trash this card. If you do, put the top card of the Mystery Pile on top of your deck.
--
Set-up: Create a mystery pile at the beginning of the game with one copy of ten random, different kingdom cards not in the supply (that cost $4 or more). The Mystery Pile is not part of the supply.
Action-Duration
$5
Area 51 FAQ: Cards from the mystery pile are not gained. Therefore, on-gain effects of cards taken from the mystery pile do not apply.
This doesn't need to be non-terminal. Also, I'd probably cost it at $4. After all, you have no control over what you get and it's a huge waste if you gain a card costing less than Area 51 itself. I have the same concerns about swinginess as the others here, but there's nothing intrinsically wrong with swingy cards, I guess, as long as they're fun.
Griffin
$0
Worth +$1 for every Victory card in your hand.
--
Once per turn, while this is in play, if you buy a Victory card, +1 buy, +$1.
--
When you discard this card from play, if you bought at least 2 Victory cards this turn, you may put this card on top of your deck.
Treasure
$5
I think this has too many moving parts. I'd keep the top and the bottom, scrap the middle, and move the +1 Buy to the top. Other than that, this seems pretty cool. Might need tweaking after playtesting, but I like the overall concept.
Goblin
(+1 Action)
Trash a card from your hand. Gain a card costing up to $4 more than it. Trash this card.
--
(When you gain this, gain a Copper.)
Action
$5
I'm not sure how this will work in practice. I think you should playtest it and see if people buy it and what they're usually trashing with it before tweaking it further.
Unicorn
Worth 1 VP for every Unicorn in your deck, including this one.
--
When you buy this card, reveal your hand. If you have any Victory or Curse card in your hand, trash this card.
Victory
$6
I worry that the VP gains from this might be a bit too explosive. I understand that the on-buy penalty is meant to counteract that, but I think it just makes it more luck-based. Do you happen to have a Victory card in your hand? Too bad. You get 3 Unicorns and your opponent gets 5, for a VP differential of 16. That's more than two Provinces!
Titan
(+1 action?)
Reveal the top 3 cards of your deck. Choose 1:
Trash all of them, draw up to 2 of them and discard the rest, or discard all of them and each other player discards down to 3 cards in hand and gains a Copper and a Curse, putting them into their hand.
Action-Attack
$6
Again, I might cut this down to 2 choices, just to simplify the card. The Attack is obviously quite brutal. I strongly advise against the +1 Action.
Conclusion: As you work on the set, I'd keep an eye on having a good balance of terminal and non-terminal Actions and be wary of cards that strongly promote boring Treasure-centric strategies.