Hello, this sounds like a scam. Instagram is a free to use service and won't ask you to pay.
Have a look here on how to avoid scams on Instagram. You should try contacting Instagram's support centre to flag up this issue.
As for logging into your account - it could be that it has been hacked, hence why you are seeing the popups. Try connecting to Instagram on another device if possible. If the problem persists look here for information on how to recover a hacked Instagram account.