Floyd roses can be difficult to set up right.
What guage strings are you using?
If the bridge is lifting up, you need to de-tune the strings untill they are almost limp, open the back compartment, find the 2 screws that hold the "claw" onto the body, and tighten those screws a little. It will move the claw closer to the body, pulling the springs tighter, and lowering the tremolo back down.
Tune the strings back up and check your progress. It may be a bit annoying. If you dont feel like messing with it, just have a pro have it professionally intonated.
And with a FL trem, its best to choose a string guage and stick with it, so you dont have to make any more adjustments when you change strings.
also, when you change strings, change them ONE at a time. Dont take them all off at the same time. Take the old E string off, put the new one on, tune up, take the old A string off. . . . .