Hello and welcome to Apple Support Communities.
I understand your issue to be with your Apple ID and the App Store. The App Store says your password is wrong, even though you have changed it and it still says it is wrong.
Have you tried signing out of the iTunes & App Store in your settings and signing back in?
Settings > iTunes & App Store
Tap on your Apple ID and sign out
Restart your device
Sign back into iTunes & App Store
Please note that signing out of iTunes and App Store will remove saved offline songs if you are an Apple Music member.
Also, here is the article for the Apple ID password. If you forgot your Apple ID password
Let us know the outcome.
Enjoy your day!