Transferring ownership over to another user only requires a "new" address on the receiver's part if the receiver is choosing not to re-use an address that they've used before. It is recommended that you generate a new address every time you receive bitcoins, but it isn't required. There is no need to create a new address when sending bitcoin, but since there is usually some "change" involved, the Bitcoin-Qt wallet (and some other wallets) automatically create a new address for that change. Bitcoin-Qt hides that address from you, but continues to track the private key and bitcoins associated with it for you.
We are dealing with abstractions here, so as an analogy what youa re saying is fine so far. In reality there is no thing called "a bitcoin". There is no magical string of numbers that anyone can point to and say "that's a bitcoin". What you really have is an output that has a value associated with it. What you spend is the entire output, there is no way in bitcoin to partially spend an output.
So lets say someone sent you 5 BTC and this is the only bitcoin you've ever received. What exists in the blockchain is a transaction that has some inputs (we'll get to those in a minute), and one or more outputs. At least one of those outputs will have a data field called "value" that will have 500000000 in it (all values are stored as integers and represented as "Satoshi's"). That output will also have a data field that has your bitcoin address in it. This output makes it clear to the entire world that 5 BTC of value can only be transferred to another address (or addresses) if a digital signature is supplied by the private key that is mathematically linked to your bitcoin address.
Now say you want to send 2 BTC to someone else. Your wallet will create a transaction with one input (since you only have one output right now). That input will have a data field that will contain a reference to the output that you received. It will also contain a digital signature created with the your private key associated with the receiving address you had used. The transaction will have 2 outputs. One will have 200000000 in the "value" field, and the receiving bitcoin address supplied by the person you are sending to. The other output will have a 300000000 in the "value" field, and a bitcoin receiving address from your wallet (to send this "change" back into your wallet as a new unspent output). Depending on the wallet you choose to use, that receiving address may be "new", or it may be one that was already in the wallet.
No. Not "a certain number". Either it is valid and peers will relay it, or it isn't and it won't be relayed.
Confirmation is different than validation. Confirmation is done by miners and consists of adding the transaction to the blockchain.
He is the owner by nature of the fact that the output can't be spent without supplying a signature created from a private key that only user B's wallet should have.
No. User B's wallet first generates the private key. Then it generates the bitcoin address from the private key. Then user B supplies you with their receiving address. Nobody and nothing except user B's wallet knows what the private key is. Each private key has exactly one bitcoin address. If anyone else has that same private key, they can generate the same bitcoin address.