3. Power level: Opening Tomb/nothing already guarantees hitting $5 during the second shuffle; I don't think any other $3/$4-cost can do that. As such, I think it's close to a must-buy, at least in kingdoms with key $5/$6 costs (and these are common)
Feast. Death Cart. Several others like Smithy and Horse Traders make it so that you only won't hit $5 with extremely bad luck.
4. Encouraging uninteresting strategies: Which strategies work best with this card? Those who rely on spamming the same card over and over - Minion, Governor, that kind of stuff.
I don't agree with this. A deck full of Tombs don't do anything for you compared to a deck full of Minions or a deck full of Governors. You still need cards that get you money, buys, attacks, etc. With a deck with lots of Tombs, you'll probably want to name Tomb when you first play a Tomb. So you get another 1-2 Tombs in hand. And you know a card or 2 that's on top of your deck, so you can safely name that for the next Tomb. But they're not going to be really good cards either, because expensive cards are discarded. So it will probably act more like Apothecary; a way to pull your coppers into your hand.
In fact, I really wonder if this will play more like Apothecary than Wishing Well. Any time you name Copper, the effect is almost exactly the same as Apothecary. Except with more drawbacks. So it has the flexibility of naming other things, but what else are you going to name that's going to be as good or reliable as Copper? You have to combo it with cards like Governor or Minion; cards that you want to play a lot of during your turn.