Anyway, should the NTC have the same value as the fast blow fuse? How should I select a replacement?
Since a fuse has its value in Amps and how fast it blows, and NTC's have a resistive value at 25C you can't say that!
Why is it even there?
Is the NTC shielding the fast blow fuse?
It is probably there to limit the inrush current, it has a (relative) high value when at room temperature, then it heats up from the current and the value goes low.
Think of what happens when you put AC on a diode bridge with a big capacitor at the output. At first the cap is empty so there will be a lot of current flowing into it.
So yes, in a way it protects the fuse, but that is not the main reason why it is there I guess.
For the replacement... I don't know. No schematics I guess, and not another one to have a peek inside?