On the bolded one, it would hold Everstone to pass down the Adamant nature, correct?
Correct. Remember it will pass down the nature about 50% of the time.
Also, for a Physical Sweeper, which 3 stats would 31 IV be the best in? Atk, Spd, and...?
Depends on what you like, or are afraid of. HP, Def, SpDef are all good choices. Also depends on the poke. Blissey likes extra points in Def more than she does HP, for example. Shuckle would be the opposite, lol.