dohnjoe

there is no other fuel filter besides the 'cup' you mentioned.
 
there is a strainer inside the fuel tank.
there is a small strainer inside the inlet pipe of the carburetor.
 
that's all.

changing gearbox oil every 60.000 km or 2 years is often forgotten. 
but as long as there was the right oil at the right level over time, not changing tl has little or no importance.
gears wear out mainly from bad shifting or from putting too much weight/stress on the car
normal driving habits keep the gearbox happy.
1) 2) and 3) are correct, but that is not the problem.
the noise disappears because the gearbox gets hotter, the metal expands and the play is reduced. no mystery.
Felicia's gearbox has a design flaw in 5th speed gears area.
there is a spot with bad oiling.
all Russian Felicias developed that noise more or less after 100.000 km
depending of driving style and load.
 
I will explain the steps of failing:
- the bearing that fails first from bad lubrication (dripping style) is this:

this needle bearing has a plastic cage.
 
see additional photos below (1)
 

 

 
- then 5th speed gears start to worn out from wobbling
- finally the outer bearing of input shaft starts to wear.
 
now you know what to change:
needle bearing for sure, maybe 5th speed gears, maybe input shaft bearing.
I hope this helps.

some thermostats are bad from new.
cheap quality, wrong temperature, bad calibration.
but I suggest short radiator fan sensor's contacts see if fan starts.
then remove short, let car idle and see if fan starts right above middle marker of temp gauge.
if it does not -> might be fan temp sensor bad if you ruled out air pockets.