Not quite. Your wallet can have an arbitrary number of addresses. You can receive at one address, then send that balance out to a dozen different people using a dozen different sending addresses.
...no. That's not how it works. Your wallet has a pool of private keys. Addresses are the corresponding public keys. You can send or receive from any address you have the private key for (minor simplification, but doesn't affect my point).
There is no transaction necessary to send money from a completely new address, other than the transaction itself. All of your addresses point to the same wallet.
Each bitcoin is owned by the public key that it was last sent to. You can't send it from a different key - it won't be accepted by the network. The public key continues to own it until a transaction signed by that public key is accepted by the network. Read the whitepaper.
