#1
will there be any problems tuning up a dropped tune guitar with a floyd rose? (tuned up correctly of course) like will it warp the neck or be twaggy?
#2
It might, if the truss rod was adjusted for string tension with a particular gauge and tuning.

For example, my guitar has always been played in standard E, or D#. The neck was perfect.

At some point I wanted to fatten out the bottom end, so I tried some light top/heavy bottoms, and after a few months started to notice a slighty increased convex shape due to the increased string tension with the heavier gauge strings being tuned in standard. I didn't actually measure the tension, but it was my understanding that heavier strings need more tension to achieve a given tuning.

I changed strings to an ordinary set of 10's, and the problem went away.