Moved to Webmail "Web and Email" forum: Emails in email app do not match webmail (IMAP acct)

Hi,
I am a volunteer working for an organization called Seniorweb PChelpAtHome.

Question 1:
Strange situation:
It involves
1. the Apple email app on an iMac running Catalina
2. the corresponding webmail account: [email protected]
If I send an email to [email protected] it shows up both in the email App's Inbox and in the webmail Inbox as would be expected.
What is odd, is that in the email App's inbox there are many many emails, but in the webmail Inbox there is just one - the one that I sent.
Yet the email account is an IMAP account.
Any idea what might be going on here?

Question 2:
I am tempted to delete the email account on the iMac and re-create it. But I don't want to take the risk of losing all of the emails that are in the email App on the iMac, both in the Inbox and Sent box.
Is there any way I can back up the emails before I delete the account?

Thanks for your help.
Andynic