Nice to see you here! I think your expansion has a lot of neat ideas in it, though a bunch of stuff looks problematic. Art and mockups look solid. As for the individual cards...
Chest:I think the concept is cool. I would change the wording though - this is kind of similar to Co0kieLord's suggestion:
You may play an Action card from your hand. If you do, set it aside.
While this is in play, whenever you would draw a card, instead, you may discard this and play the card set aside with this.
The 'you may' is necessary to not cause tracking problems (like, if you play it without Action cards in hand, there is no way for other players to know if you cheated by not setting one aside. You'd have to add an 'or reveal a hand without Action cards' to fix this). I don't think the 'otherwise, discaird it during Clean-up this turn' which Co0kie suggested is necessary, since the card should discard itself when it is not needed to remind you of something (see Haven; doesn't stay out when it didn't target a card).
Additionally, I'd suggest this change:
You may play an Action card from your hand. If you do, set it aside.
While this is in play, whenever you draw a card, you may discard it. If you do, discard CoH and draw the set aside card.
The reason why is that the 'would' wording is often problematic (more specifically: leads to non distinct and often counter intuitive interactions) and should be avoided whenever possible. This is a significant boost in power, but that should be fine for a support card.
Comic:This looks much more problematic... honestly, I don't see the concept working. It has 2 issues - first one is that it can be political. In a 3 player game, if A reveals Curse/X and B reveals Province/Duchy, do you help A to hurt B? Not inherently bad, but Dominion is non-political as a design principle.
Second is that it's extremely swingy, very harsh in rare cases, and really bad in most. Since trashing cards is good early game, you'll rarely even use it - if it hits 2 provinces though, it can kill one without giving the player any consolation. Note that most common attackers either give something in return (Swindler, Saboteur) or can't kill cards which are too expensive, like knights.
Express Tain:Per default this is a non-terminal Secret Chamber, but it has the potential to be one of the strongest cards in the game, in combination with say Council Room and any +Action. Crazy combos aren't a bad thing though, as long as they're not too common and work in a fun way. I think this could be fine. I wouldn't put it at 5$.
Bats:This
looks like it could be fun, but I'm fearful that it wouldn't hold up in practice. I agree with everyone else that it's weak; another problem though is that the thing you're investing on causes all players who use this card to benefit equally. Forager does that too - but Forager is good anyway, plus you'll get at least a copper into the trash without even trying, and the effect of boosting it kicks in faster.
Trashing other bats, though, is almost always bad for your current turn, so whenever you start doing it, your opponents can probably just buy a couple for themselves and then your investment was useless. Most decks are at least fairly flexible, plus decks are often similar, so if your deck is capable of buying them, chances are so is your opponents. I suspect that it'll be the right choice to never trash other bats in the vast majority of games.
Harmony Stone:Self-counting cards are tricky; I tried and failed at them before. I don't see an immediate reason why this one wouldn't work though - it's on the strong side at 4$ but can't cost 5$ for sure; cards at 5$ need to do stuff on their own.
Pawn Shop:I suggest this change:
+2$
You may trash this. If you, +1 Action and place the Pawn Shop token on top of a supply pile.
Cards from the pile with the Pawn Shop token cost 2$ more.
The reason is that a plain '+1 Action' is so bad (and immediate benefit so important) that you would almsot never choose not to trash the current version. This change makes it strong enough at 2$ to warrant a buy even if you don't particularly need the Token part, which will cause it to be used much more often. I also changed the wording; I don't think the 'at all times' is needed.
It's simliar to embargo, but may be different enough to be a legit variant. I also see a cute interaction with Trash for benefit (i.e. put it on Remodel, play Remodel on a second Remodel and gain a Province).
Familiy Tree:I think this has too many problems. A few you named, others are
- it's super weak (may not look that way but trust me, it is; cards which require build up are generally weaker than intuition suggests (compare it to King's Court)).
- it has tracking problems (Action-less hands)
- referencing the wording or text of cards is often a messy way to go about stuff
- the effect is probably unclear in a bunch of cases
- can probably cause infinite turns somehow
Rainboom:May be okay, but I suspect that it's almost identical to Tactician in most sets, and much worse in most sets where it's not. Usually, whenver you have a lot of options in Tactician sets, you want to play it with fewer cards than 5 on hand, not more. The biggest difference is that it allows you to integreate a few high value treasure cards into your Tactician deck, which is pretty good... might be enough.
Staff:Flavor is awesome.
The on-play seems pretty similar to Talisman in early game, which is weak, but that's fine for a 3$ with an on-buy effect. Said effect is pretty neat - if you have say an early gold, you can buy it with a hand of GCCCC and upgrade 4 coppers into silvers and stuff like that. This is actually probably the card I like most.
I'd suggest a different wording though:
Gain a Silver, putting it into your hand. Discard 2 Cards.
When you buy this, reveal your hand and choose any number of Treasure cards in it. Trash the chosen cards and gain one Silver per card trashed this way.
Top half because you want ot stay as close to published cards with your wording as possible (see Explorer and Horse Traders); bottom half because the order of resolution is more distinctly defined this way.
Sun/Moon:Uh... hm. Not sure how much I can say about the mechanic, whether or not it's good really depends on where you want to go with this expansion. On this subforum, I think we tend to judge all cards as if they try to mimic official cards (which a lot of them do), and as such I'd sagree with Asper that the mechanic is probably not worth it. That's the kind of thing which is likely to cause a ton of problems; you addressed some of them, but your throne room ruling actually seems counter intuitive to me, and the Wishing Well ruling is just kind of arbitrary. If you have different intentions, though, these concerns might not really matter.
Independent of that, Moon seems too strong and Sun a little bit too weak. Sifting 2 cards on every turn for free? That's worth a ton, and the card is very easy to get. If it was just moon, I'd say it has to cost at least 5$. And a delayed woodcutter is... well, worse than a woodcutter, which is already weak. There is a point to be made for flexibility though.
With Doctor:Im pretty pessmisitic about this one. Firstly, it's crazy strong. Early on, it'll trash 2 cards, draw 1,
and hand out curses. That's, like, quite a bit better than witch, which is one of the strongest 5$'s, so I'd put it at 6$+. It's also very swingy... and not realy in a good way. Revealing Gold-Curse-Province is just so much worse than Gold-Curse-Copper, similarly to how hitting Estate compares to hitting Copper with Swindler, which a lot of people complain about.
If you want to keep it, though, I'd suggest this wording:
Look at the top three cards of your deck. Trash any number of them. If you trashed exactly two, each other player gains a Curse. Otherwise, gain a Curse.
Wrap Up:Self-counting cards are tricky, like I said above, and yes, it seems a little strong with +Action - it also looks a little weak without the +Action though.
I'd suggest this wording:
+1 Action
You may trash a card from your hand.
While this is in play, whenever you trash a card, (you may (?)) gain a card costing up to 2$ more than it.
It might also be worth considering to have the coin difference scale, rather than the number of cards gained. Like, 'gain a card costing up to 2$ more per Wrap Up in play.'