I had an unfortunate accident with my 20 year old Fiat Punto.

So - I'm sending you some photos with the most important damages for the expected reparations. In addition, the cooling water was drained through a broken pipe, but that is the only problem associated with engine functions. Please also note that I bought and temporarily attached a front bumper.

Taking into account the front/front-right body sags, damaged front lights as well as the broken cooler pipe is it possible to make a reasonable reparation (I mean to fix the front body sag/deformations without necessarily to replace chassis parts) ?

pretty hard to say from pics, it looks superficial damage but you need to find out if the chassis is still straight, if it is then its just a matter of replacing the bent panels for new or bending them back - depends how fussy you are about it being perfect.