1) There are six cycles a day:
AM Part 1: around 3am
AM Part 2: around 7am
PM Part 1: around 11am
PM Part 2: around 3pm
PM2 Part 1: around 7pm
PM2 Part 2: around 11pm
Games are played only on the Part 1 cycles. Other events, like free agent responses, coach hiring responses, trade completion, etc., can happen on all cycles.
2) On arbitration day you'll be able to make your arbitration offers. You'll see what they are asking for, and what a "typical" player with similar experience and stats is making. You can avoid arbitration by either signing the players to a long-term contract (or by releasing them) before the hearings.