I seem to have it figured out. I bought a clone Note 3 back in December 2013. Worked just great, until April 2014, when it started doing the random shut off/reboot and I thought I was because of the clone, and then I read that regular Note 3s were doing this too. So I did the hard reset: did not fix it. Thus, I removed the back cover, and when comparing with online pictures, I realized that one of the little screws were missing. I took a little screw from another location and put it in where one was missing: it fitted. Thus, for some reason the screw got loose and fell off, or maybe it was not there in the first place ... anyway. Then, I decided to check if all the other screws were tight, so I checked each one of them and some of them indeed were somewhat loose (particularly the one in the top left corner). I tighten them all with an adequate small-size Phillips screwdriver, not too tight though because I did not want to mess up the plastic thread. I used the phone long enough after that to conclude that it was now working just fine and not shutting off/freezing/buzzing/restarting randomly.
BOTTOM LINE: Solution is to remove the back cover and tighten all the visible screws in the back of the phone.
UPDATE: Phone is actually still freezing/re-booting/buzzing. Phone became useless. It must be a bad phone ....