(Cause I already experienced a shortening on a cheap SATA to IDE converter that basically burned the wires to the supply with a bit of smoke etc... I would like to separate this thing in case something goes wrong from the entire system supply or other peripherals).

A resistor should be enough, but sure, a fuse can't hurt.

How to calculate kind of resistor or fuse?

Its just LEDs, so you have some freedom (higher value resitors = dimmer LEDs). From the specs (5V, 60mW) I assume each segment can draw up to 12mA, therefore the entire circuit can draw up to 84mA with all segments on, but I don't think you'll find such small fuses (100mA). I'd try some sub-1k resistor and see if it works well.

From the datasheet it says Peak forward per segment 80ma, continuous forware current per segment 25ma.

First rule of LEDs is to always use a resistor. If you put a LED directly to 5V, too much current flows through it and it heats up and fries itself. It won't melt any PC power supply wires I assure you.

If you quote the datasheet, 25mA per segment is the maximum safe it can work forever. As you say the LEDs read "40", that's 10 segments? 250mA. Yes, there are 100mA fuses, but it is not enough. In real life, you put a fuse to protect your PC power supply and its wires, the PSU can give out 10-30 amps. Also, it is there to protect the target load from heating up and burning. In this case, I'd say 500mA or 1A fuse, but as I said, it only protects from a short circuit.

Also consider how bright the LEDs are at 25mA, when you have 10 of them blazing. It is possible it is bright enough at 5mA or 10mA.

So, you need a resistor to limit current. Please see the following link : https://en.wikipedia.org/wiki/LED_circuit. As you see, the resistor size depends somewhat on LED forward voltage which depends on LED color. It is easiest if each LED has its own resistor, but if you are feeling to solder less resistors, you can put 2-3 LEDs in series, but it will be more difficult to balance their brightnesses. You can also put LEDs in parallel, and have a single resistor, but depending on manufacturing tolerances, one LED could be brighter than others, and some may not light up at all.

Thank, I already put a resistor (red-white-brown-gold) in each positive segment being the cathode shared. But my fear was as you said certainly for any short circuit that would target the supply and the wires as I already risked with the bad experience of the sata ide converter (for another pc and a supply also quiet expensive...).

Even if one of the LEDs short, you'll still have the resisor there limiting current. I wouldn't worry about it. I mean... those LED panels in old Baby-AT cases do not have any form of protection besides resistors, and they work just fine.

If concerned about one section shorting, maybe use a 10 ohm 3 watt resistor in series with the lot - that would limit the overall current, but it will also take the brightness down a bit

Well I went for a 250ma fuse on the positive end so it should be enough at least for the supply/wires, the led are not important but the only at supply I have now yes...and I think I will put a resistor too as you said. 😁 Now mounted it is running quiet cool and bright! I still have to put some trasparent black plastic on to it but this "40" strong led on the front is nice!
I will post the result!