you can get away without any clamps if the board you are gluing is exactly the same shape as what you are gluing it too. clamps just make the two pieces conform to each other. obviously if both pieces are warped, its going to take more clamps to get a professional finish. and always leave wood glue for 8-12 hours, preferably over night, to dry.
you can use any bi-metal hole saw to drill thru both metal and wood (i believe the size for drilling shank holes is 7/8", but double check first). for gluing a piece of wood to a metal fridge, i would use some construction adhesive and probably a lag bolt and nut all the way thru on either end of the board (and maybe a couple in the middle) to give it some stregnth. nails are for wood only and have no stregnth in metal.