Most marketplaces use a very similar upload process.
You must provide the data they need so that they can do two things: (1) send your masterpiece to a blockchain and (2) provide viewers who are potential buyers with information about your masterpiece.
OpenSea upload - part A
The upload process is relatively simple. There are instructions with most steps. You can link to a website and provide a description to help sell the item.
OpenSea upload - part B
You may be able to upload unlockable content that is only available to the buyer or choose the blockchain you want to use to sell the item.
OpenSea marketplace – Buyer view
The digital file is usually stored in one of two places. If you have used a centralized marketplace, then they are most likely holding the NFT on their servers and you must login and ask them to transfer it to you if you want to move it. If you have used a decentralized marketplace, then it is most likely the file is stored on a blockchain and you can access it via your wallet.
The smart contract code creates a permanent record. So once it has been executed (minted) some of the NFT information becomes metadata and this cannot be changed.
It is OK to save a copy of an NFT that you own to your mobile or another device. Some people display them in digital frames on a wall. The original is still linked to your wallet.