I keep getting a message saying that I have a virus on my phone, and ones that tell me my passwords are at risk. What should I do?

If these are messages from the calendar, see:

If running iOS 13 or earlier versions, check: Settings - Passwords & Accounts - Accounts - Any rogue entries here? If so, delete the rogue account. 

If running iOS 14, check: Settings - Calendar - Accounts - Any rogue entries here? If so, delete the rogue account. 

You are welcome.

If you found a foreign calendar when you checked, and deleted it, it will indeed help.