Universal Building Code - Roof Pitch?

No minimum pitch in the code. Required slope would be determined by roofing materials. Most shingle type roofs require minimum 4 in 12 pitch. You can go as low as 2.5 in 12 with special underlayment. Some local jurisdictions with heavy snowfall require a steep pitched roof for obvious reasons.

I would have the pre-fab home company include a clause in their price proposal that the roof pitch must meet UBC. That puts the responsibility on them to meet the code. Then have them state on the proposal what that pitch is.

4/12 is the lowest pitch I would go on a straight hip or gable roof. I suggest 5/12 on any roof that has intersecting gables or shed roofs coming off of it.

If you are generally handy you should be ok, look for some websites 'shed building' garage building to give you ideas. Aim for about 15/16" below the guttering of the higher roof to have room to cut the flashing in. You will need to remove the existing roof to give access to the wall plate at the far side of the garage. If your old outbuilding is getting 'old and past its sell by date' check that the wall will carry the weight of the new roof. Attach a 4X 3 " wall plate to the higher wall and notch the rafters over it, ideally spacing them so they fit the dimensions of the covering you are going to use