A game like Stardew Valley would be quite do-able in Unity.  As for performance, you just need a semi-competent programmer and you should be fine.  Unity has been used to make hundreds of 2D and 3D games, much like the Unreal Engine.  Honestly take your pick, either will do fine.  As for others, I'm sure there are a lot of other engines, but what is your or your programmers language of choice?  Unity uses C# and Unreal uses C/C++ and Blue Prints.

You just have to look at Unity showcase to see whats possible here. 

Its just up to the capabilities of you and anyone who works with you. Depending on your skill set other game engines might be better suited but Unity is in no way incapable of producing the type of game you are making.

Inquire on their forums or post questions here about your "issues".  I doubt Unity has problems rendering 2D tiles.  I also doubt you need a hack to "fix" it.  I suspect it's a lack of experience more than anything.  Games like Pillars of Eternity and Wasteland 2 were made using Unity.  Wasteland uses 2D tiles for the ground and it's a AAA game.  I would stop listening to rumors to be honest.  They're typically started by inexperienced people or trolls.  If there are actual problem, people will post evidence and the Unity or even Epic's teams are fairly quick to jump on any real bugs.

Unity is 100% capable of making a Stardew Valley clone.  Just like Unreal Engine is.  Game Maker is rather amateur-ish at this point though could likely also do a Stardew Valley clone as it's not a very taxing game (could likely easily run on older mobile platforms to be honest) since it was used to make Crashlands which works on mobile too.  But I'm not sure if it's free either.  Again, you asked for advise, we gave it.  It's for you to ignore or accept.

If you have technical issues with using any of the mentioned engines, make a new post.