Funeral
Action - Attack
Cost: 5$
+2$
Each player (including you) reveals the top 2 cards of their deck and trashes a card that you choose.
Random trashing means it's swingy. Offering the choice of 2 cards means it's targeted randomness. Zero in on the Provinces and win. In a mirror match, worst shuffle luck loses.
Indiscriminate trashing is no fun, let alone targeted trashing. At minimum, the victim needs to get some form of compensation proportional to the loss. Observe how Saboteur and Swindler accomplish this.
Exorcist
Action
Cost: 4$
+1 action
Look through your discard pile and trash up to 2 cards costing 2$ or less.
This is possibly fine. I suspect it's a lot more powerful than it looks, though, and might need either a price boost or the loss of its +Action. Most trashers weaken the buy phase by trashing cards
from the current hand. Two are exceptions: Loan, which is a decent card despite being limited to Treasures and fails once you start buying better Treasures; and Masquerade, which is such an elite $3 card that it would make an elite $4 card.
But we also have to consider that you might draw this at the top of a shuffle, in which case it's useless. So maybe $4 is fine.
I'd drop the price restriction, though. I don't think it adds any real gameplay. Most cards you want to trash cost $2 or less anyway, and when you want to trash a card that costs more, that's an interesting strategic play that should be allowed.
Coffin Maker
Action
Cost: 3$
+2$
+1 action
You may trash a card form your hand.
This is largely equivalent to a Silver that lets you trash -- as such, it's terribly underpowered. $5 is probably the right cost, as that's where Silver-with-a-bonus cards usually belong. You have more wiggle room, though, given that this is a Silver-as-Action rather than a true Treasure. Still, it's a pretty sweet card at $4, for the same reason as Exorcist is: with the cash bonus, it offers trashing without crippling your buy phase very much.
Cantor
Action - Attack
Cost: 5$
+1 VP
+1$
Each other player gains a Curse.
It's an interesting idea. Cursers are strong primarily because they clog up your opponents' decks, not because of the VP penalty. But here's a cursing card that exaggerates the VP swing. So that's obviously strong. But what it does otherwise is only +$1, which is inferior to Witch's +2 Cards. So maybe that balances out.
The key difference, however, is that Cantor is more useful after the curses run out than Witch is. Given that Witch is already one of the strongest $5 cards in the game, it should probably raise a red flag if you are proposing a $5 card that's probably better.
Graveyard
Victory - Reaction
Cost: 3$
Worth 2 VP.
When you buy this, trash a card from your hand.
When you would gain a card, you may reveal this from your hand. If you do, trash that card.
This should probably be "when you gain a card," rather than "would gain," although it might still be fine. My problem here is that I don't understand its overall utility. How do the different pieces synergize? By the time you want to buy victory cards, you probably don't care much about trashing. And if you buy these early to make use of the trashing, the trashing effect is negated by the fact that you're replacing whatever you trash with a mostly-deadweight green card.
It's entirely possible I'm not foreseeing a cohesive use of this card, but I do think it's important that these sorts of "do a little of everything" cards synergize together. Like how all the diverse effects of Watchtower and Jack of All Trades combine to undo the effects of most attacks. Or how Steward's list of choices allows it to remain useful in all three stages of a typical game (trash in the early game, draw in the mid-game, money in the late game).
Crypt
Action - Victory
Cost: 4$
Worth 1 VP.
+1 card
+1 action
Look through the trash pile and choose a card costing up to 8$ that is not a Province. Gain a copy of that card. If the trash pile is empty: +1 card.
Edit: I misread this card at first. See Jack Rudd's response for a great verbalization of my own thoughts on this.
Lost Diary
Action
Cost: 5$
+1 action
Reveal the top 4 cards of your deck, put all revealed action cards into your hand, discard the rest.
You could make a persuasive argument that this card's average case is better than Scrying Pool's average case. Scrying Pool obviously has a stronger upside -- no limit on the number of action cards you can draw into your hand, plus one non-action card -- but you only need to draw 2 total to make Lost Diary as good as a Laboratory (better, actually), and the potential to draw more is really nice.
Anyway, Scrying Pool is good enough that its purchase needs to be limited by its Potion cost. So I worry that this would be too strong. But there are enough differences that maybe this is okay. If you ever playtest these, let us know how this one works out.
Edit: I didn't notice that the other cards are discarded. That definitely makes it too strong. The ability to cycle past junk (and if you're playing with this as a strategy, you're probably not buying high-value treasures, in which case it IS junk) is very very strong, which is why Cartographer is a $5 card despite doing nothing for your current hand.