Hi VirginiaWood,
welcome to te Apple (user-to-user) Community
Re: "No matter how many times I have tried to reset my user email and password, they will not "stick" even though I get emails saying they have been done".
Sorry to read that you are having such trouble. Am no expert in this area, yet your post deserves some response. We are all Apple users, like yourself in te community, so we have no access to your accounts or details in order to check this out for you.
You were able to sign in here to the community ok ... those same details are likely to be in use in the App Store, and in use for FaceTime, Messages etc..
You can check if any App Store restrictions are set:
Set up content and privacy restrictions in Screen Time on Mac - Apple Support
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Seems your iMac may need updating to the newest compatible MacOS version.
(Eg: For MacOS 10.15 Catalina that would be MacOS 10.15.7)
You may see if an update is waiting to be installed in System Preferences > General > Software updates.
If so ... it is wise to back up your Mac data safely before updating.
Else if already using the newest compatible MacOS version, and you haven't already tried it,
Try re-starting your iMac : (deletes temporary files, re-establishes connections, often updates recent setting changes, and often restores order if something is not working).
Eg: Go to: Apple Menu > Restart, wait wile Mac restarts, and log back in.
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Re: No matter how many times I have tried to reset my user email and password, they will not "stick" even though I get emails saying they have been done.
Wondering where you are trying to change te details ... in the App Store perhaps.
Your Apple ID is the one account (now called Apple Account) that you use to access all Apple services and make all of your devices work together seamlessly. ie: The Apple ID Account gives access to the App Store, iCloud, iMessage, Apple Music, Apple TV+ and more.
If you need to change your account log-in details:
You can log-in online, to check or change your account details so they are up-to-date.
https://account.apple.com/
or
If you forgot your password you can: Reset your password at iforgot.apple.com
and
See how to: Change your Apple Account primary email address - Apple Support ie: your log-in ID (if not a phone number as used in some countries)
You may need to allow 24 hours for any account changes you made to be updated everywhere they are in use.
(Else: Restarting your Mac may help details update)
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If you have difficulty getting a verification code:
See: If you didn’t receive your verification or reset email - Apple Support
or
how to:: Get a verification code and sign in with two-factor authentication - Apple Support
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Re: I need to go to the App Store, specifically, but it won't let me sign in.
If more trouble-shooting is needed:
On you Mac: See if you need to: Sign in to your Apple Account - Apple Support
and
See how to: Sign in to the App Store on Mac - Apple Support
You can choose how often you want to enter your password when you buy items
If you don’t want to enter a password when you download free items, follow the steps in the article and turn off password protection for free items:
Require a password for purchases in the App Store and other Apple services - Apple Support.
Eg: says:
Require a password on your Mac
- On your Mac, choose Apple menu () > System Settings.
- Click [your name].
- Click Media & Purchases.
- Select the settings that you want for free downloads and purchases. If you have Touch ID turned on for purchases, you won’t see this menu.
What to do: If you can't download or update apps on your Mac - Apple Support
All the best :-)