I know you need to have a certain skill in somethign to be able to place perks in it, but does it give any benefit besides that? Will I hit harder and more accurate with "h mastery at 40 compaired to 20, or is the only differeance that I can put more perks in it? If it does give an added benefit, what are they and how effective are they. (also for armor, lockpicking, alchemy etc).
Yes, I think it does. Higher skill in, for instance, one handed, will make you deal more damage and lose less stamina for attack from those weapons.
Does benefit or sleeping add any benefit and if yes what?
Yes, being rested/well rested gives you experience gain bonuses.