That's a little misleading... the payments arrive immediately when the block is found. They are generated coins, so they show as "Immature" in your wallet. You must wait the 101 confirmations before you can spend them.
Depends on the wallet? Or maybe I never really checked into it too much.
I run Bitcoin core as my wallet. Every time we hit a block my balance didn't increase until all confirmations were done. Now maybe the funds were "there" before but didn't show and I just didn't know how to discern the difference?
It's not wallet dependent, however many wallets (and exchanges) do not handle generation transactions correctly.
The 100 transaction wait is built into bitcoin core, and all nodes using the reference client will reject transactions that try to spend a generation transaction before the 101st block after they were generated.
An example of this is TREZOR, originally it would try to include generation TX's before they had 101 confirmations and the transaction would be rejected by the network and held in limbo on the mytrezor site indefinitely.
They fixed their UTXO selection to correct for the problem, and now it works fine.
Edit: You can always check you mining address on a reputable block explorer, also my site will show all p2pool earning to any address that has ever received a p2pool reward:
http://minefast.coincadence.com/miner.php
so less than me ... payment still happend 2x per month only. 
checked the wallet and no payment came inn 
. I point p2pool to another address as p3yot33at3r described earlier. In either case, that address exists because p2pool needs to know who to pay any fees to, and also who to pay if a miner is mining on your node with an invalid BTC address. 
