Our ability to advance troubleshooting on this site with an iPhone is extremely limited. You already did everything reasonable in an effort to resolve the problem. The next step would be to contact Apple, who can remotely view your iPhone — with your consent of course, and assuming it's even possible given the problems you're experiencing with it. In the end you may need to take your iPhone to an Apple Store so that they can see first hand what's going on with it.
Start here: Official Apple Support
You will of course have to be patient as they have you repeat everything you already did. Then, they are likely to ask some probing questions that probably shouldn't be discussed on this publicly viewable website, after which they are likely to come up with additional suggestions. If they strike out you'll be invited to make an appointment at an Apple Store.