I've just got a Jackson RR3 Snow White Pinstripe Edition and I see two problems with that guitar.
1. I can hear a guitar even if i put a volume pot to 0. This concerns both pickups. Also, if I don't play anything, I can hear buzzing.
2. If I use tremolo bar to pitch up note, strings are touching bridge pickup. What can I do with that?
Should I be afraid?
1. It may be that the electronics need to be replaced. If you can solder then it would be a cheap fix. Just buy the right pots and a good cap and you should be good. Also, get a new output jack.

2. I am no Floyd expert but it sounds like the bridge is way too low or maybe the pickup is way too high. Try lower the pick up height some. That might give you enough space without sacrificing the magnetic field's strength.
1. I played today on Blackstar HT-60 and it's buzzing only on cranked gain channel.
2. I have just regulated it and I see the E string must go little up. Then all will be good.