Yep, i think it is impossible to complete the game. But it is fun to see how far you can get. I would guess it stops at cosmo canyon, but we will see.

No weapons accessories, only what you start with as you enter team
No materia
No items
and ONLY in game heals.

Examples where there is hp recovery, is after the first mission, just before Cloud meets Aeris, he's hp is recovered.
When they rest at Aeris' and Cloud sneaks out to continue alone.
When they depart, after they sit on the toy thing and Aeris runs off to the mart.
Etc.

As of now i am lvl'ing outside Kalm.