Yes, pools feed your miners work.
What do you mean by "filter blocks"? You don't send blocks to your ASIC. In fact, your miners have no concept of a block whatsoever.
The "block hit" process happens if your miner provides a solution to the SHA256d hash which satisfies the network difficulty. There is no such thing as "whole block calculation". There is only SHA256d hashing.
Because he's creating the block (just like on my pool, I create the block). As such, I can define what transactions are in the block, including the coinbase transaction (the one that defines how/where the 25BTC block reward is distributed). On his pool, he defines the coinbase transaction as "99% of the reward + transaction fees goes to address XXXXX and 1% of the reward + transaction fees goes to address YYYY".
The network handles block difficulty. All difficulty means is, "the solution you provide must meet or beat this value in order to accept your block on the chain".