I have similar experience... Spent already 70K on my Auto cuore in less than a year. Will sell soon. If you want peace of mind then another car please, but drive quality of cuore is good. If we'll maintained, even cuore is a nice car but it's very sensitive to any alterations.
Don't mess with temperature guage your fan was on direct, so the seller did that on purpose because the car was overheating. Your mechanic probably removed direct fan and made it auto. The last time this happened on my car head gasket blew twice. Get all head work done and only then convert car fan back on auto.
A good Engine oil for cuore engine in good condition is Castrol Magnetic 10W-40. Change every 3-4000 km.
Don't install HIDs in old car, they can fry your engine electronics specially if the engine bay is altered like yours. Cuore headlights are infact very very good, get yours checked.
Fuel economy on AC is trash but on normal it gives 10-11 km/l in automatic. In manual you can expect 12-13km/l .
Cuore was also my first car a year ago, I recommend you downgrade to a mehran as your first beginner car; it can handle much more abuse. Alto is also not a bad car.
If you want to follow my journey with all the problems and solutions in my car you can see cuore automatic maintainence schedule: