Hi, I'm new here
Anywho, I'm having a bit of a (maybe noobish) problem...
I took my guitar to my mother's home, and I as I took it out of guitar gig bag,
a string snapped, so I decided to remove them all and install a new set (They were pretty old).

So, as I removed each string one by one, everything was cool, until I took the
last one out, that's when the floyd rose tremolo came unhinged like it shows in the picture
below. I tried to install new strings, but the tremolo just would come up...

Is this normal? I heard that is ok to leave it flushed against the body, instead
of floating...

I just want to know if it's ok like it is or what I can do...

Step 1: Remove string. Step 2: Replace. Step 3: Repeat as needed.
Tiger style.
What you are supposed to do is to take off a string, then replace it, then take off the next. In your case, just stick a block of wood or something under the bridge so that it is lifted.
Agile 3100 CSB
ESP MH400 w/ Trem-Setter
Epi G-310
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1968 Fender Vibrochamp - Great amp, only $100 fixxer-upper
Line 6 Spider II

You shouldn't have taken all the strings off at once. You can get it working again, but it's a pain in the arse. I realised this after I rebuilt my Lo Pro Edge on my RG.

What I did was held the trem up against the posts and blocked it in the trem cavity behind, then strung up and tuned it up (while keeping it on the posts). Always make sure the Knife edges are on the mounting posts properly. Once you've got it so that the strings have enough tension to keep the bridge in place, remove the block, tune up and adjsut as necessary.
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In this case, loosen your trem claw springs. Then dive down the tremolo bar and insert a pen cap or 2 here.

Then your bridge should be about parallel and continue to stringing -> tuning step.
"Play with your ears" - Yngwie Malmsteen, Paul Gilbert
Thats what she said...