The harder the lock the longer it takes. A higher skill (or use of perks) would make picking quicker across all locks. All locks should be attemptable but locks far outside your skill should take a while to pick.
Picks should be very rare but never break. If you are arrested they are taken from you. You can find them but they should be extremely rare in loot tables, rare to find placed in the world and sold by appropriate factions (Dark Brotherhood and Thieves Guild) but should be fairly pricey. Because they never break it's pointless to buy multiple unless your getting a spare to keep at home.