Noob has questions on repairing roof.

I doubt you can repair the ceiling to any where near showroom finish. I'd suggest to mount a metal plate, a light fixture, or some other material across the hole. If you're considering using Styrofoam bead board, that is the worst choice, IMO. Styrofoam will separate and you'll have white beads over everything, always. Extruded polystyrene is similar in weight but is a better material.

The roof would typically be fixed by repairing the wood sheathing and installing an EPDM patch or covering with Eternabond tape.