Q&A for How to Get Push Notifications for a Users Tweets on Twitter for Android App

If you want notifications when anyone tweets (not just a celebrity), you have to go to that person's account, then select the bell icon near their name. Once you do that, it will give you the option to be notified when that specific person tweets.

You can only get notifications within the Twitter website if you don't have a phone number.

Try force closing the app and reopening it, and if that doesn't work, delete it and reinstall it.

Yes, you can.