Hey there WLG15,
We use our iPhones daily and can understand your concern when it's not working properly. Let's see how we can help get that issue resolved.
We'd like to first send your attention to this great guide to what all the symbols and status mean for your iPhone. You can check out that guide here: Status icons and symbols on your iPhone
For your issue with notifications not showing while you're on your phone, we'd like to have you check out this great guide to ensure your settings are correct: Use notifications on your iPhone, iPad, and iPod touch
If you continue to have issues after check out those great guides, reach out to use using this link: Get Support
Cheers!