Behavior on Crash and Recovery

Even if we view the committee as non-changing, I understand that we want the system to behave properly even if some honest parties crash and recover.
I'm not sure what state is retained (if any) between a crash and recovery.
It seems like very little state is retained.
By "retained", I would mean written to disk in some solid, "journaled" fashion.

I'm worried about corner cases, such as the following:
1. A node crashes and recovers, and now proposes a second vertex in the same round. To the rest of the committee, this would appear to be incorrect behavior.
2. A node crashes and recovers, and even though it had sent an ACK for a message M it had previously received, it has completely forgotten about M and ACK. Other parties who received the ACK will not know that they need to resend M.
3. A node crashes and recovers, and it sent a VOTE for a proposal in a given round and from a given party before crashing, but after recovery, it might send a VOTE for a different proposal from the party in the same round. (This relates to another issue I raised, whre I pointed out that a party really should only vote for one proposal per round per party).