Will Outlook sync the email accounts to another PC when logging into my MS account?

Have integrated on my computer my email account in Outlook. If I now install Outlook on my laptop and log in with my Microsoft account, will the email account be automatically included? And must there manually add the email account?

No.

You have to add this manually.

It is important that you rely on IMAP and not on POP3.

With POP3, e-mails are usually downloaded by the e-mail provider. On the server then no more emails.

But: Outlook can't do IMAP really well. It works, but not nice.