1) I think that cupboard and cabinet are nearly interchangeable, certainly in kitchen use; Otherwise, a cabinet might tend to be a bit fancier, perhaps more for display purposes than simple storage.

2) The pronunciations I use are cubberd and clabberd, although CLAP-board is not unknown. I've never heard CUP-board except humorously.

3) I believe that the board in cupboard is a shelf on which cups are set or stored; clapboard is overlapping wooden siding for a building, so, again, it's literally a board.

Peter