I'm totally unconcerned about squire being bad with Lab and Smithy. So what? Every card doesn't have to have synergy with every other card. And just because you really like using those cards for engines doesn't mean everyone else does, or that there's no room for other kinds of engines. Where I am really concerned is about it being not useful enough often enough, and too strong when it is good. But I'm actually not so concerned about that even. The best kind of combo among what you've pointed out looks to be some kind of village-vault-squire, and that will give you $5 and a 5-card hand. Well, I'm not too worried about that, 'cause it's a 3 card combo from three different sets which doesn't totally break the game anyway. Well, okay, village could be any village, vault could be secret chamber (I don't understand how cellar is really that good here)... maybe you're right. We'll see in playtesting.
Vault/SC is the meanest case, but it's really good with all ~15 basic non-terminals. Pretty much any of them at all, from Fishing Village to Upgrade--then you've also got village combos with hand reduction actions like trashers and BM. All this is maybe too good for a typical $2 card, sure, but it's not the end of the world.
The issue is how mediocre it is with everything else. Like, in the absence of those really great cases, it's just pointless. It's a draw engine card that you can't build a "real" draw engine with. The idea of an engine is to power through your deck faster and get to play more stuff. Typically this means drawing your entire deck, which this card is counter-productive dead weight against. You could almost imagine it working like Minion which is sort of a weird alternate draw engine, but Minion only really works because it combos with itself. This card is only really enabled in that sort of way by a couple cards, unlike say Smithy which can build a draw engine with any of like 15 Villages.
I mentioned Celler because it's a good non-terminal lets you churn though your deck and find more hand-reducing non-terminals like it.
Servant's village: Unexciting? Maybe. I'm okay with that. The comparison here is fishing village, which it is except for the duration, which almost always makes it worse. But then it only costs 2. I'm not concerned, though it's obviously not spectacular. Again, playtesting will help.
I'm just not understanding why this card exists though. It's not that it commits some cardinal sin--it's that what it offers isn't something I as a player want in my deck. Normally if you offered me a random $2 card for free during a game of Dominion, I'd take it--only exceptions might be Moat, SC, and Herbalist about half the time. But unless unless there's no other Villages at all and I badly need one, I'd never take a free +2 Actions +1 Coin card. (Just like I wouldn't normally take a free Copper.)
Bronze: Well, I've already posted my thoughts above. I expect even with the modified version, it's not going to be all that great all that often, but I do think it is interesting enough. We'll see - needs playtesting.
Your changed Bronze proposal is a lot more docile and has a lot of fun utility. It's a worse but functional Haven that gives you $1! This is great because Haven is great. This version is not a self-perpetuating super strategy, and instead has fun plays and interactions with all sorts of other cards and decks.
Novice
Action 2
+1Action
Gain a card costing up to $3
I'm not sure why this costs $2? You are right about the variance, but it's not a big enough problem to worry about--you are still going to have semi-interesting $3 options on a majority of boards. Non-terminal Silver gain is nothing to scoff at.
This is a really powerful pile-emptying machine of course. Like, to a kind of absurd level that slightly outpaces even Ironworks. That's not innately bad, but it's something to consider. Again, $2 is probably too low, else +Buys compound the effect pretty hard.
Renew
Action 2
+1 Card
+1 Action
Discard your deck.
Chancellor doesn't do much because as an opening Chancellor is your more valuable card, and a terminal blocking other valuable cards. A $2 non-terminal Chancellor is super powerful. I'd buy it at $3, for sure.
Assassin
Action-Attack 2
+$1
Every other player reveals their hands. Choose a card for them to discard. Then each player draws a card.
Ew, targeted discard. I think someone else mentioned that Donald wrote some stuff on why this was found to be a dead end filled with hurt feelings and tears. It's high variation, kinda slow, and encourages bland, defensive deck construction.
Also this is *crazy* strong at $2! Throw some Villages with these bad boys and man--they better have good trashing or hands are going to suck.
Oh, and multiplayer games are just going to get obnoxious with this, in ways Torturer and friends can only dream of.
Thinkaman: Some great observations all around. I'm not sure I entirely agree your aversion to mixing money and villages, though. Villages are engine cards, and the ultimate goal of an engine is to accrue money, so if the engine cards themselves generate money (see: Minion, Bazaar), then that's a good thing, right? But you're right that it would be one of the last choices for a Village-type card, because the modest $ boost isn't worth the drawing loss.
The catch is that money on a cantrip is a different animal than random money on some card like Chancellor. That's why Peddler, Treasury, Market, Grand Market, Bazaar, and Conspirator are so great and cost as they are.
Besides Lighthouse and Fishing Village--which are as they are to be satisfying Durations--there is only one non-terminal card in all of Dominion that gives money without +1 Card. That card, Festival, is a special case built around a +Buy; giving money with Actions doesn't make total sense, but a +Buy is an interesting resource and what goes with +Buy? Money! It's not random money thrown on, it's a built-in Woodcutter.
The +Buy on Festival is like pancakes--pancakes are good with chocolate, and they are also good with bacon, so maybe we can have all three at once. (Even if chocolate and bacon alone is still unnatural and weird.)