These cards have some truly great ideas in them. My feedback:
Beggar- $2
Action
+1 Card
+1 Action
You may trash this card. If you do, return all cards in the trash to the supply (including this one).
Not convinced it'll work, but it's probably the best idea for trash interaction that I've seen. Since the purpose is not to gain cards from the trash, you've managed to bypass the primary problem, which is that sometimes there are Colonies in the trash but mostly there are only Estates, Coppers, and Curses. I still think there is a problem with it being too situational, though: how often does three-piling happen as a result of trashing, as opposed to simply buying up cards? Sometimes there isn't even a trasher available. True, Beggar can trash itself, but since it bounces out of the trash the second you put it in, its power over even the beggar pile is extremely tiny.
But you can address that by making Beggar itself a trasher of more than just itself:
Beggar
$4 - Action
+1 Card
+1 Action
Trash a card from your hand.
You may trash this card. If you do, return all cards in the trash to the supply (including this one).
Now you've got a card that fills the trash at will as well as being able to empty it.
Guild Hall- $3
Action
Choose one: Place a guild hall token on a kingdom card supply pile that does not have one OR Remove a guild hall token from a supply pile OR $2.
_
While a guild hall token is on a supply pile, that pile does not count toward ending the game.
Pretty slick idea. I think it needs some constraints, though, or as someone else pointed out you could King's Court this and fill up the whole board with guild hall tokens and never end the game. Maybe a limit on the number of tokens you can place. I'm thinking maybe only 2. I also think there ought to be a mechanism to speed up the game, too. For starters, you could give out the +$2 bonus always. Compared with other $3 terminal silvers (Woodcutter, Chancellor, Fortune Teller, Swindler) such a card seems quite reasonable. That would encourage people to spend more money, thereby depleting piles faster, but I'm not sure if that's enough without playtesting.
Holy Village- $3
Action
+2 Actions
You may trash a card in your hand.
I like this as-is. Diving Pikachu's recommendation that it mandate trashing a card is duly noted and is important to consider when playtesting. But I guess my intuition is that it's fine the way it is, mostly because +2 Actions by itself is so incredibly weak: weaker than Native Village, for instance, which only costs $2. In other words, you're not going to buy this card unless you intend to make use of the trashing. Or, I suppose, if you're incredibly desperate for a Village effect and don't mind that this one stinks and probably isn't going to be enough to get an engine to fire.
Bounty Hunter- $4
Action- Attack
$2
Each other player discards an attack card or reveals a hand with no attacks.
I don't like this at all. For one thing, not every game has attacks, so if this is the only attack card in the kingdom, there's no reason to buy it. But even so, when this is on the table, you don't buy attacks, and when nobody's buying attacks, you don't buy this either. And if someone buys up attacks anyway, this attack will sometimes do nothing and sometimes hurt more than basically any other discard attack in the game. So it's swingy, too.
Exchange Market- $4
Action
Choose one: Place a token on the Exchange Market mat OR remove a token from the Exchange Market mat OR gain a card with cost up to the number of tokens on the Exchange Market mat.
This is another cool idea. I like the idea of a manipulable shared resource. On the surface, it benefits all players equally (as does Trade Route), but the reality is that it benefits them differently based on what their strategies are, how many of these they have, how often they get through their decks, and so on.
But again, I think it needs tweaks. For one thing, you'd have to play this 3-5 times before it becomes really interesting to anyone. And who is going to spend 3-5 actions (in a game that might only last 15-20 turns!) building up something that will then be equally powerful to
everyone? Basically it would be a mistake to ever put a token on the mat, because then the benefit to your opponents comes free, while you had to spend a card slot and an action on it.
Instead, how about this?
Exchange Market
$4 - Action
Gain a card that costs +$ equal to the number of tokens on the Exchange Market mat.
Choose one: Place a token on the Exchange Market mat; or remove a token from the Exchange Market mat.
--
Setup: At the start of the game, place three tokens on a shared Exchange Market mat.
I actually wonder if it wouldn't be better still to disallow the ability of removing a token. In that case I'd start out at two tokens on the mat. As is, I think there is still a real disincentive to boost it up to $5, because then your opponent could snipe a $5 card and drop it back to $4. You could also provide a bonus when you boost the card that you don't get when you drop it, like a simple +$2 or something.
Anyway, I'm sure this idea can work with the right tweaks. Very cool.
Inquisition- $5
Action
+1 Action
Place the Inquisition Marker on an Action Card supply pile other than Inquisition, or set it aside.
_
While the Inquistion Marker is on an Action Card supply pile, copies of that card may not be played (the Inquisition Marker begins the game set aside).
Like others who have replied, I'm not a fan of this card. I don't think it's a tweakable thing, either: it's just not very fun to be prevented from playing cards. Plus, there are rules problems: if you supposedly can't play Minion, what happens when Golem turns up two Minions? Do you break Golem's rule, or this card's rule? It's an unresolvable situation.
Raiders- $5
Action
+3 Cards
Trash a card from your hand. Trash cards a number of non-victory cards from the supply equal to half of its cost rounded down, split between any number of piles. Then trash a non-victory card from the supply.
I can't envision in advance how this one would play. Normally I'd say supply trashers are too boring and situational to be worthwhile or fun, but I like the idea of tying the number you can trash to the sacrifice you make in your own deck. And the fact that this is a useful card even without taking full advantage of the supply trashing means that this isn't going to be a situational card overall. But it's impossible for me to predict how it will tend to play out.
Wilderness- $5
Victory
At the end of the game, if one or fewer piles in the supply are empty, this card is worth 6 VP. Otherwise it's worth 1 VP.
I like the idea of a victory card whose VP value fluctuates by the number of empty supplies. I've been considering something like "Worth 2 VP per empty supply pile," for example, though I haven't worked with the idea long enough to determine which formula would work best.
This is a lot riskier than a simple formula, of course, because buying up the last Pearl Diver could turn your opponent's Provinces into Estates. That's pretty serious -- I don't like how swingy that is, even if it's swingy in a way that a good player ought to be able to foresee and control. Duchy-to-Estate might work better, or, alternately, a Estate-to-Duchy, going the other way. I dunno. By all means, experiment with the idea.
Army- $6
Action- Attack
Each other player reveals any number of cards from their hand whose combined cost is $6 or less, then discards the rest of their hand.
I love the idea of a discard attack that cares about card costs, but I'm very unconvinced that this is the right balance. You're telling me if my hand is Throne Room, Conspirator, Silver, Estate, Estate, I get to keep only the Silver? That's a shut-out, too powerful to price at any cost. Seems like the cap needs to be much higher. On the other hand, even as is, I could keep all of my cards if my hand were Gold-Copper-Copper-Copper-Copper, so I worry that the attack will be too swingy no matter what the cap is. Some other nuance to the rule is needed here to regulate the card's power, but heck if I know what that might be.
Altar- $7
Action
Trash any number of cards from your hand. If the combined cost is $1 or more, +1 card, +1 action. If the combined cost is $4 or more, $2, +1 Buy. If the combined cost is $20 or more, at the end of this turn, the game ends.
I think you need to lose the "end the game" piece. I mean, I see how that's how the card fits your theme, but I don't think it'll play out in a particularly satisfying way. But I do like the idea of a trash-for-benefit card where the benefit not only escalates as you trash more and more valuable cards but broadens as well. Transmute is sort of like this, except that it looks at the type of card you trash, rather than its cost (which is what Salvager, Apprentice, Bishop, and Trader look at). This card sort of combines principles of both to make a new card that is its own thing. I don't know if this is the right set of limits and bonuses, but the concept is sound.