OK, in order, here is what I think will happen:
1. Posey will opt out (pretty much a no brainer), but the C's will sign him to a 3 year, $15 million deal (he will have some offers of 4 years, but at less money per).
2. Tony Allen will sign the one year tender. Teams very rarely sign restricted FA's to offer sheets...especially not ones like Allen. No team wants to tie up part of their MLE on him at a crucial time in the FA period, when there is a chance the C's will match. The only way he will be gone is if the C's can use him as a salary in a trade.
Of course this could be effected by the draft as well. If a wing like Brandon Rush or Chris Douglas-Roberts falls to them, it makes Allen very expendable, and they may try to package him to bring in a backup PG or big.
3. Eddie House will be gone, unless he comes back for the vet minimum. They are not comfortable with him as the backup PG, and they have a cheaper (and already signed) option waiting in the wings as the 4th/5th guard in Pruitt. It is tough to give up the veteran presence, but if they are giving Posey a raise, it would be tough to swallow giving a raise also to House (which is what he would probably want), when they really only want him to be a 10 minute per game player.
4. All three of these guys are probably gone. I think they will look for an upgrade at the backup PG (or more importantly, someone they can count on not breaking down). They may bring back PJ, but for some reason, I anticipate him retiring (especially if they win the title).
I expect the majority of the MLE to go to signing a replacement to Cassell or PJ (or maybe split between the two). The top targets will probably be Kurt Thomas, as well as Chris Duhon, Anthony Johnson, and Anthony Carter.