TPMS Light Notifying Malfunction in system

370zHawaii

I have 2011 with about 350 miles, drove it to Waikiki steady 70mph for about 15 minutes, light came on while I was driving and freaked me out, I slowed down to 60mph to grab to owners manual, thought I was going too fast as the motor still has low miles, found out it was this TPMS light, what a relief! Weird though because after driving at 60mph for about 5 minutes the light went off. This was this past Friday, I drove it today (Monday) and as I started my baby up she blinked for about 60 seconds and stayed on But I just checked the tire pressure all tires read about 40psi, I read somewhere that the dealership intentionally over inflate tires because some cars are sitting so long, I am going to drop my tire pressure to the recommended 34psi and see what happens, if this does not correct the problem I am def taking my baby to the dealership, I have some questions maybe a Guru could answer for me
1. Will the dealership charge to correct this problem?
2. Is this covered under warranty?
3. Is there a Diy fix/reset for this, specifically for 370z (I seen the Diy for the G37)
Thanks & aloha P.S I am a newb so take it easy on me