I don't have a floyed rose BTW!

When I go to use my trem bar, for the first time after tuning immediately after using it I hear a small click sound... no idea what it is or how to fix but i know its not supposed to be happening..

Also by click sound i mean its like hitting something, its a thudish sorta sound coming from the bridge i guess.
is it the ball ends of the strings shifting in the bridge?
2003 Fender Standard Strat w/ Texas Specials
2012 Babicz Identity Dreadnaught
2015 Gibson Les Paul Traditional SR
Line 6 POD HD500
Peavey XXX 112
Fender Blues Jr
what guitar?

sounds like something moved when you had the strings off and has slotted it self back in, has it done it again.

could be the block hitting the body as you used the bar, take the trem cavity cover off and look inside whilst depressing the bar
I think you're just pushing the bar too deep. My friend had the same problem and turns out he simply pressed it too much. The click comes from the springs on the back. relax, you don't have to lower each note an octave.
yeah, those vintage tremolo's aren't really made for true divebombs. it's probably the trem block hitting the guitar inside... not sure what else it could be