Really cool ideas here!
Obviously the Adventurers themselves are only half the story, but here are some thoughts.
Barbarian: The issue I have with this is that it only slows the game down, and it only comes into play if there's another attack - which will already be slowing the game down!
Cleric: I think this needs to do something if it doesn't trash a Curse, like give +$2 or something. Bring back Chancellor! As it is it just doesn't really do very much, it's not even particularly impressive at trashing Curses.
Fighter: I think this is a much more successful Attack-Adventurer than Barbarian. I appreciate the simple effect, although adding yet another additional component to all this isn't ideal. I wonder how often you don't open with this though, it seems like a very good opening.
Sorcerer: I've read the other's comments on this and I don't really get what they're talking about. This is just a fancy Village right? It just sort of Band of Misfits the card it plays. Having said that I do quite like this one, most of the issue I have come from the cards associated with it.
Wizard: So when I first read this I thought it was a very type restricted Remodeller and really liked it. I like it less now that I've read it properly though, it doesn't really seem as interesting to me. I am admittedly a Remodel-junkie though, I love those things!
Onto the cards themselves.
Circus: I'm in agreement with Commodore Chuckles that this really doesn't need to be a Treasure as is. I'd argue that the cantrip part of this is already one of the better $2 cantrips so it doesn't really need the help either. However if it's Adventurer was Wizard then it being an Action-Treasure would actually be relevant and that would be really cool, I'd also bump up the price to $3 so you can gain a Gold with Wizard if you made that change. I get that this is a nice $2 so helps out a Fighter opening, but I don't think Fighter opening really needs the help.
Goblin Ambush: This is really similar to Cutpurse and Fighter is already very similar to Cutpurse really. You also have a card that's pretty much just Sea Hag too.
School of Magic: The issue with this kind of thing is that it doesn't work without a non-terminal Action. This adds Wizard to the game though which is a non-terminal Action so that helps. I feel like this should set aside from hand though, it makes it work in more kingdoms and less likely to be broken.
Tomb Raider: I think this is a little too good for a regular $5, but I guess Cleric makes it worse because there's always the Curse trashing. But man Cleric just seems really weak the more I think about it so I'm not sure. I also feel like this should be a Warlock or some kind of Witch type person, Cursing other people doesn't really seem like a Tomb Raidery thing to me.
Corrupt Noble: I absolutely love this card! But I still have a little problem with it, because it's paired with Sorcerer I thought you'd be able to make Nobles cheaper and then use Sorcerer to play a random crappy $2 or $3 cost as a Noble, but you can't do that. I suggest making it change cost in all phases to accommodate this interaction. I also think it should probably cost $7, it basically costs at most $5 as is because you'll always have at least 1 Buy if you're buying things and I think it should be a bit overcosted when you only have 1 Buy. (I know Margrave and Wharf exist, but +3 Cards +1 Buy really is a $5 effect.)
Dark Priest: This is fine but it needs to reveal itself, just copy the wording on Tunnel. I still think Cleric is kind of a dud to be honest, I feel like discarding your whole deck and triggering all of these won't be as satisfying as making use of Tunnel and Faithful Hound can be.
Dragon: I don't really think we need another Sea Hag, I don't really think we need one Sea Hag to be honest it's a bit of a dud. I don't like having Fighter paired with an attack because that's supposed to be Barbarian's thing. I also feel like we don't need 2 Cursers in this batch of cards and I prefer Tomb Raider over this myself. I also find this type of effect that involves lining up specific cards ends up being cool to read, but playing really badly. Think Urchin or Mountebank's Curse blocking, it just exacerbates shuffle variance in a really visible way and leads to unsatisfying games in my opinion.
Monstrous Lair: I appreciate that Gold gaining can hedge against Barbarian attacks. The stuff I said about Dragon kind of applies here too, you can't even gain more Adventurers to try and control lining things up better, you just have to hope you draw your cards in the right order.
Hidden Treasure: The Buy restriction seems like a worthwhile thing to try, but Gold for $5? I think we're well past the days of anyone caring about a slightly discounted Gold.
Pendant: I kind of feel like getting 2 free Coffers and Villagers with your Wizard is sort of crazy? I'm not really a fan of having such an obvious and automatic interaction baked into a card like this to be honest. The card itself seems fine though, I usually like how these types of things play.
Pegasus: I'm not sure why this makes Horse not work. I guess it's for flavour purposes? But your Adventurers can ride 7 Pegasus if they want, so I'm not sure why they can't ride a Pegasus and a regular Horse.
An overall thought on this set of cards is that the effects seem pretty unbalanced. We have 2 junking attacks and 2 handsize attacks but only 1 trasher and no real villages, no remodel and no non-Gold gaining aside from Wizard. There are 6 terminal Actions and 5 non-terminal cards, which is far too many terminals. Whether you're bothered about this depends on whether you want this to be like an actual expansion or just a collection of cards I guess.
I think having things called Adventurers and Adventures isn't a great idea, having things with such similar names can be confusing to people (mainly me). Why not call them Missions? I also think a lot of these will be very snowbally. For example, the first person to gain 4 cards in a turn will usually be the person in the best position anyway, so giving them 2 more Coffers than everyone else will just extend that lead even further. I think these would play better if everyone gets the same bonus for completing the task, and they'd be simpler too which is win-win. You'd probably have to scrap the Ruined Crypt, but I think that one needed changing anyway. I'm assuming you plan on having 10 Adventures so there's one for each Adventurer pair?
The Equipment are my least favourite of these mechanics to be honest, for a couple of reasons. It seems like they won't really have a huge impact on most games because you'll often only have 1 Adventurer and they don't really add all that much. They also add a lot of complexity to what is already a relatively complex mechanic. I get that it's flavourful, but we already have Pathfinding et al from Adventures so this type of card modifying effect isn't particularly new or novel anymore. The other thing is that Dominion is all about variety, so having the same 4 Equipment every time seems kinda lame to me. I'd suggest just having one Equipment per game, but having 10 or so different Equipment so you can have a different one every time. That way there's less to take in all at once for someone first playing with Adventurers and there's more variety in the long run, maybe you can buff up the effects a bit then too if there's only one at a time.
Hopefully you find my comments constructive.