I had exactly the same problem myself! I was away on vacation and the phone's ringtone would randomly go off despite there being no caller, then the car mode would launch every two minutes ( I don't even have a car!) I read online for a couple of solutions and nothing seemed to work, (but you can disable car mode from the settings of the app by disabling the auto launch features - it won't stop the phone ringing though). Then the host mode message began appearing! I figured maybe some intense heat from my vacation had damaged my phone.
I eventually decided to call HTC as I'd even try to do a factory reset and that didn't work. HTC were the due to pick up my handset the following day and so I'd left the phone switched off for a good 18 hours or so I, anyways, I then went to finally wipe the phone of any personal data and somehow it's worked fine ever since. In the end I'm not actually sure what happened to the phone but it's working fine now. It was at a point where it wouldn't even charge unless turned off, and even then that didn't always work.
Maybe leave the phone alone and switched off for half a day or something, then factory reset it and see what happens. Believe me I've scoured Google and android forums looking for an answer to this but there doesn't seem to be one, I fixed mine purely by change. Failing that I'd give HTC a call, it's not ideal I knowl, but it's clearly a common fault (there's several others post on forums quoting the same issues) and so you should have no problems with a replacement, especially since the handsets not even been around a year.
Hope this helps.