Initially, as I was reading I was thinking that your locking mechanisms weren't engaged on the G string... then you said that they were tight. So, that leads me to believe that when you, or whoever, was stringing your guitar they didn't pull the string completely through. Sometimes strings can get caught on the wraps instead of the bob at the end... most of the time when you're tuning the guitar up the string will achieve a certain amount of tension and it will come loose and you will simply have to keep winding the tuners until it is tight... However, in rare cases the string can catch in a spot that can withstand the tension and won't budge once string tension is applied. This causes severe tuning instability. That is my current diagnosis for you tuning problems. I suggest taking the string out and re-stringing it with a new one.... As for the noise, Floyd Rose trems are mechanical devices, they have moving parts... when parts move in conjusction with other parts, you get some noise. The noise won't transmit through your pickups though... so don't worry. The only time you have to worry about trem noise is if it's a harsh grinding or scraping noise. Slight noise is common in trems that haven't worn in yet. Good luck...