1. You can rollover once per year per account currently, but they (the government) are thinking of changing the rules so you can only do one rollover per year PERIOD even if you have multiple accounts. So it'd be to your advantage to do your rollovers as soon as possible.
2. The management fees depends on what your accounts are invested in (the funds themselves), not just what the accounts/account types are. So if TIAA-CREF is managing your accounts and they're listed there, you should be able to click into each account and see what funds/allocation you have, and click into each of those funds to see the expense ratios or management fees. Index funds should be extremely low (less than 0.2%), other funds will probably be around 1% and you should try to reallocate to index funds if possible.
3. If the accounts are listed separately, they are managed separately, even if the same institution is managing them. You can "rollover" them into one account, which you should.
4. Depends on the account types, but most accounts like 403bs, 401k, etc can be rolled into a traditional IRA. Your annuity plan is special and can't just be rolled over into another account type, it is a financial product you have purchases and you'd have to look at the cash value etc if you are thinking about getting out of it.
This is all my best understanding as I know it, but I am neither a tax specialist, nor a financial planner, nor an attorney, so the advice is worth exactly what you paid for it (hint: zero). But this just how I understand things to operate.
