A subname is a name created one level under a name you own. For example, shop.yourname.eth is a subname of yourname.eth. A subname is a full ENS name in its own right. It has its own records and its own resolver, the contract on the Ethereum network that answers questions about it, and it can have its own owner. It lives inside the parent name, so it lasts only as long as the parent stays registered.

You create subnames in ENS Explorer, and you must own the parent name. It is a two-step job: first set up a subregistry on the parent (a contract that manages the names under it), then create each subname inside it. The subregistry is where you set the rules for your subnames: who can claim one, what it costs, and how long it lasts. For the steps, see Create a subname in ENS Explorer.

By default the wallet that creates the subname owns it, unless a different owner was named when it was created. On ENSv2 a subname is an NFT (a token one wallet holds at a time), so transferring it is a token send from a wallet. Giving someone a role (a permission to act on the name) does not move ownership. A subname under an older, wrapped ENSv1 name is held a different way, in the Name Wrapper contract, but ownership works the same.

Not from ENS. There is no registration fee on subnames, because the parent's owner decides the rules, not ENS. A project that hands out subnames under its own name may charge its own fee; that is the project's decision. Many communities give them away.

Yes. A subname can be your primary name (the name apps show for your wallet) just like a .eth name. So alice.yourname.eth can be what apps show for Alice's wallet. See What is a primary name?

It depends on how the parent set up its subregistry. Some parents keep the right to renew, change or remove subnames; others give that up for good. See What can the parent of a subname still do?