How do I properly renovate the concrete floor of my balcony?
Below is what I would do, based on my understanding of what it is you're after achieving, please let me know if I get something wrong eg Have misunderstood anything or have missed any of your questions (I believe I've covered all of them below).


  From above comments: When that is covered, I want to pave the balcony with small garden rocks, I have already bought them, they are flat, glued to some farbic sieve in squares.



I'm going to assume a total thickness of 25mm (1inch) for the above material, and you know how to attach this material to the new concrete top slab. Please correct me if I'm wrong on those assumption.
I would say you want to end up with a minimum of a 50mm (2inches) step down from top of sill to finished balcony level.
Totally clear the balcony, work area (size: 710mm x 319mm)



  Do I need to clean/set up those metal parts, cover with something, to stop rust and not let the flexibility of metal handrail shatter my new layer.



Prepare and clean the existing metal hand-railing:


Use a wire-brush, steel-wool, wet &amp; dry sandpaper to remove as much flaky/loose material as possible.
Wash down everything with a mixture of warm water and washing (dish) liquid. Rinse off thoroughly with clean water. Allow to dry, then wipe down with something like White Spirit (paint thinner).
Paint (primer) everything with a rust inhibiting primer.
Then paint/spray everything with one-coat of a good quality exterior enamel.

Prepare and clean the 90mm thick balcony concrete slab:


Refer to this question here on SE for some details/information on how to go about tackling this.




  How to set up concrete "box" (to make concrete stay in place, and stop it falling off the balcony sides), there is hardly place to connect any temporary wooden box for that, ideas?



Seeing as the balcony isn't that big (size: 710mm x 319mm) you could use something like, "Bar Clamps" or "Pole Clamps" (2 would be enough), to pin (clamp) some shuttering material to the outside faces of the existing balcony concrete slab (against the 2 shorter sides). This would probably be easier and safer to do from the balcony below (if your below neighbour would allow you that access).
Make sure the side shuttering has a "slight" fall on the top face (over a distance of 319mm, 10mm would be enough), so that the new concrete will slope away from the door (sill), thus allowing any water to drain away from the building.
You could then attach shuttering material along the front face via connecting it to the side shuttering pieces.



  Do I need any layers between building panel and my new layer?



Paint the top face of the existing balcony concrete slab and up the face of the sill with 2 coats of bitumen paint. This will provide some protection to the existing concrete from moisture penetrating down from above.



  Which concrete should I use?
  How thick should that layer be, how many sacks of that stuff will I need (will give balcony area m2 later)



If going with 50mm of less, use something like: QUIKRETE&#174; Sand/Topping Mix
If going with 50mm of more, use something like: QUIKRETE&#174; Crack-Resistant Concrete Mix
For your situation I think it would be best to go with the "50mm or less" option.



  How thick a metal armature will be enough for this job?
  Wire diameter of bought armature (in picture 8): ~0,9mm



That will be fine, just place a single layer in the middle of the new concrete top slab you pour.
After you finish installing your "garden rock fabric" and have allowed everything to dry properly, I would:


Have a "general" clean-up of the whole balcony area.
Paint/spray a second-coat of the good quality exterior enamel onto the existing metal handrailing.





Good luck, and please let me know if you have any questions related to what I've written above.