Newbie Question: ERC721 and transfer

Smart Contracts
1

Question:
I am building a simple market place for 721s.
Using Metamask or some ERC20 compliant wallet and after minting and transferring an NFT token from the Minter/owner to Wallet #1.

  1. Is there any restriction from transferring the same NFT, by the owner of Wallet #1, to another new owner, Wallet #2.
  2. Does the 2nd transfer hit the ERC721 contract or is it completely independent of the ERC721 contract?
  3. Is there a way for the 2nd transfer to call the contract.

My assumption is that once an NFT is in my Metamask Wallet, as long as I can afford gas, I can transfer that NFT to any other wallet?