Transaction and Node Proximity Questions Say I am a node (M1) in the bitcoin network who wishes to spend some set of bitcoins (T). M1 selects address (A1) with an associated node (M2) that he wishes to transact with and uses some process (F) involving T's private key to sign over T to A1 to be controlled by M2. 

My question is how does T get broadcast to the bitcoin network? What model does the software enforce to announce a transaction has occurred? How is this message relayed and what kind of bandwidth does the relay require? Do all nodes reach participate in the transaction relay or just some? How does a miner decide to verify transaction T during his block solution hunt? How many transactions are considered to be a minimum for a block and how many are considered to be a maximum? And finally how long does a miner wait to fill his transaction queue for a given block solution hunt?
You add the transaction T to your (the sender's) unconfirmed transactions pool. From there on, it is treated like any other transaction. Then, your client will send a "inv" message to it's peers saying it has a transaction with hash H. (H being the hash of T) If the peers don't have it, they will send a "gettx" message requesting it, and your client will send it to them. They then add it to their list of unconfirmed transactions and they will do the same thing with their peers.