The minimum angle depends on the covering material, fixing method and the backup membrane.
There is no problem doing a hipped roof on a square building, its just the top sheets get a tapered cut
Most houses are "square" so I'm not certain where this arose - are you thinking of the detail at the meeting point?
If you want a pitched roof with no cuts in the sheeting material consider a monopitch.
A double-monopitch is next up, and I think this may be what you're thinking of.
Low pitch monopitches may have a problem if they're not securely fixed.
The roof covering/ structure can blow off, as it can flat with roofs.
Double-pitch or hipped roofs tend ot be more secure in this regard.
The detailing of the foor, its covering, insulation, support structure all bear on the cost.
Unless you submit a fully detailed design for costing to a QS or go out for costing to a contractor, you won't get a useful or reliable answer.
ONQ.