Is it possible to learn 'Fortify Enchanting' Enchantment in game? I have yet to come across any gear that do this in my 100+ hours playthrough.

No, because it sets up an infinite loop. Bethesda has learned since morrowind's alchemy loop.

Or not since we have the restoration loop, but I believe that is a bug, not developer intended.

Nope.

Thanks. I'll go & do the item improvement exploit now then. I was waiting to get some fortify enchanting gear before I did this.