I see that you're unable to update the software on your iPhone and that Messages is also not working. Keeping your device up to date and being able to use your apps is important, and I'd be happy to help.
Let's start with updating the software. If you're unable to update over the air using Wi-Fi, then you can update using iTunes.
Update your iPhone, iPad, or iPod touch
If after updating you're still having an issue with Messages, reply back with the answers to the following questions.
1. Does this happen when you're connected to Wi-Fi and cellular data?
2. When did this issue first begin?
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Have a great day!