My iPhone would just randomly give me a blue screen and then restart--did that a bunch of times between Tuesday and last night. As of last night, it WILL NOT come back on. iTunes says it's in recovery mode....what does all of this mean???

Tuesday night I was texting a friend and when I went to open her message, my screen went blue and restarted. I just wrote it off as weird and went on about my business. Later that night, I tried to turn on my phone and it would not turn on. I plugged it up, held down the power button, and pressed the home button all numerous times. I looked online and it said to do a "hard reset" by holding down the power and home button at the same time--my phone then came on. Throughout Wednesday, it would give me a blue screen and restart--nothing major just really annoying. I took it to the local Verizon store where I bought the phone from and he said that it was some type of hardware defect and I was still under my year warranty so I could get a new one for free--the free phone won't be here until tomorrow, Saturday. I took it home and it didn't give me any trouble for a couple of hours. The next day it was cooperating and then I left town for a little while and it acted up (blue screen and then restarting) a few times. When I got home, it acted up again and so I restarted the phone and it was working fine. A few minutes later, I tried to check my messages and the phone was off again. No matter what I do, my phone will not come back to life. It had at least 45% battery last time I looked at it. I decided to plug the phone up to my computer and see what it did--my computer recognizes that there is a phone hooked to it and it says that it's in "recovery mode". It also said that if I'm having issues with my phone, that I need to reset the phone via iTunes. I guess the questions that arise are

1. Why is my phone doing this?

2. If I reset my phone, will it go back to working again? I ask that because I don't want Verizon to charge me $300 when they send me the replacement phone and I won't need it (assuming that the phone decides to work once it's been reset).

3. What type of hardware defect is this that is causing this issue, not only with my iPhone 5S but others as well?

4. Shouldn't people be notifying Apple and letting them know that they need to fix this issue?

5. Should I report this issue to Apple even though I didn't buy the phone directly from them, but through Verizon?

Any help that anyone could give me would be greatly appreciated! This whole situation has me stressed out and seriously confused.