No items, you need to sell them.
You keep your 12 slots of Personas, but you must re-summon them from the Compendium. You will not have level restriction though. Your money does pass though.

Nop. No Calendar... just weather report. Although you can see (but not check) a small P3 Calendar on Souji's (MC) room.

Double summoning is gone.

At first, Diligence is best to train with Sports... you will only really need it for Tower, later in the game, and for fishing. Just work on at night when you have everything else maxed.

Its just there to be annoying. It doesn't really do anything.