Just because battery was a smaller physical size , should not have done that to the ac/heat system . You should check around the battery and see if a wire was damaged and caused a short . Smoke and smell leads one to that conclusion .
Apparently this " mechanic " wasn't smart enough to do this one wire at a time ? It does sound like firing order is way off or he screwed the timing up some how . Bet if you quiz him , he will not know this is a Chevy engine and not a Buick .
Until motor freezes up . But why keep running it ? All you are doing is making sure the crank cannot be turned to rebuild motor . Everytime that crank goes around , a little more metal is eat off .
There is a dye that you can put into the system and if not in a hidden spot , will be able to find that way . If dye doesn't work , you will need to take the car to a shop so that they can use their "sniffer" .