Having trouble with this. I don't understand where Outlook stores emails. It is Microsoft program, does it store the emails on the computer?
That's up to you.
If it's an Exchange account, the emails get stored both on the server and the local computer. If it's an IMAP account, ditto, I think, probably with some options. If it's a POP3 account, then possibly ditto, depending on how you configure it, although most people, and by default, delete messages from the server as soon as they've been read.
If you set it up to leave a copy of the messages on the server, and the provider of your server has a limit as to how much disk space you can occupy, then you'll run into that limit eventually.