Heya, I may need some more information to help understand what's causing the issue.
Your Messenger app needs to update, when you tap update it prompts for your Apple ID and password. You enter those but then it asks for an iPlayer password. I'm not familiar with iplayer passwords?
You then reset your Apple ID password but then it does not accept that password and asks to be reset again.
Okay. Let's start by checking your Apple ID and password is working.
Can you log into your account at https://appleid.apple.com?
Do you get any messages that your Apple ID is locked or disabled?