Thoughts:
Lost Arts:
This seems really, really powerful. Smithy seems perhaps the best, because Double-Lab is so very strong, but really there are lots of cheap actions which this will be very good on. Pawn becomes Village-or-Peddler-or... yeah, that's pretty good. Pearl Diver even becomes Village-with-upside. Any Moat-like card turns into Lab-plus. Terminal silvers are much more meh, but even there, this is ok. Spam Monuments or Swindlers or dare I say Goonseseses? Yes, please, at least if I couldn't otherwise. Really it seems to me like in games with this, very often you will race to accomplish: Setting this, driving the very-undercosted pile you've set it to, maybe trying to contest the pile your opponent has set. +Buy will be big for that pile-drive, especially setting it on a cheap thing, which often I guess you should. And then we're looking at pretty quick 3-piles. It's worse the more expensive the action you want to hit is, but well, it's not bad on expensive things exactly. It seems like usually it will totally shift that game around. I suppose turning Village into Super-Village isn't the hottest sometimes, but even that can be very nice sometimes.
Borrow: In a vacuum, this doesn't seem great, since a card is usually better than the money. On the other hand, now is more important than later. Obviously if I am ending the game, the next turn won't matter. If I am getting hit with a discard attack anyway, this is somewhat mitigated, but not entirely - the ability to look a card deeper is a real thing for sure. Against a sure Minion attack, this is pretty free, and against a sure Pillage attack, it's even a benefit. Also, you could just use this to make sure you don't trigger a shuffle at some point, if you've tracked your deck very well. And of course, sometimes that extra $ is really worth it, because e.g. 5 is so much better than 4. So the flexibility on this will make it reasonably powerful, even if on average the effect is really not worth it. Really not a gamebreaker, but quite nice utility.
Inheritance: Hehe, I had the idea of turning victory cards into... I think it was just copper, quite a while back. This is surely a better implementation. 7 is a lot, so this will be somewhat hit-and-miss. I mean, if you can trash the estates away somewhat efficiently, that's got to usually be better. If you can't, though, especially if you can spike this early, it will be pretty nice. It gets three junk out of your deck in one fell swoop, plus gives you an efficiently-costed, points-laden pile of something. All of this assuming, of course, there's a somewhat spammable pile of cheap actions which isn't already empty.