Wall between House and garage is hanging over the concrete slab. Is this a major issue?
It is only an issue if it is load bearing.  If it is load bearing then you cannot have part of your footing floating (in the first picture it definitely looks like the bottom plate is outside of concrete).  Period.  Is it a thing that has to get fix right away?  No.  Engineer will give you advice on fix.  It is just a wall though and shouldn't be too costly.

If it isn't load bearing it is still horrible workmanship.  I would like to see what engineer says - since we are only looking at 2 small pics - but I would say that at the very least you run a 2x6(ish) from ground to bottom plate and anchor 2x6 into concrete.