no the tuning is very stable, the guitar normally stays in tune for days, if I don’t take it outside the house. Also, when you use the vibrato modrately, the strings do not go out of tune. If I do heavy divebombs, so that the strings are totally slackened, then of course it may get out of tune a bit. But this is quickly corrected with the fine tuners behind the bridge. Even if the strings would detune themselves very strongly, you could retune the guitar very quickly thanks to the quick opening/fastening lever on the locking nut.

I never had problems with broken strings due to vibrato use. I had a few snapped e-strings once in a while, but not more than normally expected if you use 009 strings.

I sometimes had problems with a few dead spots on the e-string, but nothing which a thorough setup of the action couldn’t fix.