Had a really old bathroom fan removed and installed a new Panasonic one. When wiring it, we were not able to put the wire nuts in the fan's junction box because the wire was just not long enough (we tried pulling just a little bit but it's the most we can do).
So my first question is : is it safe to put the wires back as shown in the picture? And if not, what would be my best course of action to make this safe? Please note that I'm in a condo, so no attic access.
Cables can only have their sheaths removed inside junction boxes. A fan or similar equipment will often have an integral junction box for making connections. This must be fixed.
It appears that there is a few inches of cable sheath visible towards the right side in picture one. Assuming that is indeed the case:
You don't want the new cable way too long, but a little longer than absolutely necessary will make the installation easier.
While a junction box inside the ceiling is normally not allowed, it is normal to have a junction in the ceiling above equipment (lights, fans, etc.) where the junction box is 100% accessible as soon as you remove the equipment.
However, checking a little further, it looks like probably some combination of (a) my memory not 100% as to what is/isn't permitted and/or (b) a lot of stuff out there that isn't 100% code-compliant. The normal rule for junction boxes is "accessible without tools". An exception is made for junction boxes attached to a device - but that is not the case here, or rather it is with the original fan fixture but not with my solution. There is an allowance for boxes way up above a drop-ceiling with cables down to fixtures installed in the ceiling, but that is not the case here either. Or for a junction box behind an appliance - e.g., in the back of a cabinet where tools are needed to remove the appliance but the box is permanently installed in the cabinet to service the appliance. That last case is close to this, except in that case the box is not simply sitting in the ceiling but is inside the cabinet that holds the appliance, which is a little different.
The end result is that my solution is a lot better than the existing situation, but the junction box accessibility could still be a real code issue.
A slight variation from a comment from Huesmann, which should be 100% code-compliant, is to find a ceiling location that the existing cable with sheath can reach and put a box there with a plain cover plate. Run the new cable from there to the fan. That results in an extra blank plate on the ceiling, but if the plate is painted (or naturally if white plate and white ceiling) to match the ceiling it won't be very noticeable.
One other solution is to install a very large box such that it can reach from the existing cable sheath on one end all the way over to where the fan wires exit the fan's integral box on the other end, and screw everything together. That should be 100% compliant, but would like be a real pain to install.
Also, as noted in another comment, condo, so no attic access is a real concern as well. In most jurisdictions work in a multi-tenant building must be done by licensed electricians.
What you have is not safe and not to code.
You already have holes in the ceiling. Look into the holes and see if there is a staple holding the cable to the fan. If you can, remove the staple and see if that gives you more cable to work with. If not, you need to move the fan closer to the cable end and the connections must be in the junction box and have an strain relief and insulator in the hole.
You will need to have the ceiling repaired anyway. Move the fan so the electric connections are safe.
Install a small junction box flush with the ceiling somewhere along the route of the existing cable, and pull the cable into it. Splice another length of cable long enough to easily reach the fan to it in the box, and wire up the fan. Neither wires nor cables are allowed to enter holes in metal boxes or equipment without a suitable clamp/grommet, as your photo shows. There are cheap little plastic cable clamps that just snap into the holes, available everywhere.
