My guitar will not stay in tune at all when I use my original floyd rose trem bar ever since I changed the string gauge.

I play in drop c (CGCFAD) with 11s.

When I dive bomb most of my strings go sharp and when I pull up they go flat.

I have 4 springs in it and the trem is level so it can't be that.

Oh and also, my strings don't all drop down correctly when I dive down. The highest strings drop but they don't get loose like all the other strings and flap around. Dunno if that's part of the problem or what but I thought I would mention it.

I put in the 4th spring myself and made it so the trem is even. I have two springs at 1 side and two at the other.

What could the problem be?

Check the locking nut, make sure the strings aren't sliding around or getting snagged. You knife edges may be dull as well, check that out.
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What the hell is a G&L.

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Gay & Lesbian I think, the box smelled funny
Greg what did you send me??
What are the knife edges?

They shouldn't be dull because I just got this guitar last month...or at least hopefully not.
Take off locking nuts, ok now plug in a tuner and leave the guitar, 2 minutes later, come back and check whether the guitar is out of tune if it is retune it and then come back and repeat the process until the guitar goes out of tune much slower, or even holds tune. Put locking nuts back on and finetune it, then start playing.

I done that and my guitar hasnt gone out of tune for at least 2-3 months... and its a ****ty guitar too.