With HOA Approval of the structure, yes.  There are some standard building requirements, please review the HOA docs for the specific information.

No.  There are some metal sheds that have been installed, but they have not been approved by the board.  The covenants state that sheds / garages must be built of "like materials" of the house which means brick / stone or siding depending on the location of the structure.

No.  We do not reserve the pool, it is open for resident use during its normal operating hours.