I know that just don't know if the dealer can Reclaim all costs from fiat HQ like first two years
Yes they reclaim all the costs. However being a dealer they get paid a "Fiat Labour" rate which is normally less than their public hourly labour rate.
Unless you are in a position to do more detailed mechanical inspections then I would just let these be done by the MOT and 3rd year service.
What you can and should do is go over the car with a very general close visible inspection. Some areas to look at:
1) Paint work especially in recess areas such as bonnet, tailgate, doors, etc.
2) Trim Outer fixings - are all the plastic trims, like around the outer windows all sitting down and properly seated, and for any chrome ones still looking good
3) Trim Inner fixings - door cards, pillars, etc. Tap them for rattles etc.
4) Water Ingress - check boot well and accessible areas - e.g. behind any removable covers for changing rear light bulbs etc. Also in the driver/passenger floor area you may have a plastic pop-up flap in the carpet to allow the floor pan chassis number to be inspected (is it dry in there). You could find other areas to poke around without removing internal sill trim to get your hand in under the carpets. e.g. the holes in the carpet below the driver and passenger seats where the seat wires come through
5) Engine bay - check that all the wiring looms, pipes and components are in good and secure condition. It is not uncommon to find something that has been rubbing against something and left a visible mark or minor wear
6) External lighting - go round the car tapping the light units. On my 500X I had a fog/corning lamp which worked OK but when tapped rattled badly. This Fiat replaced with no hesitation
7) Electrical - check that all the windows, interior lighting, puddle lights, etc. are all OK as these are outside of MOT checks
8) anything else you fancy. Just have a good poke around all over the car