I finally got to cleaning the camera. I have cleaned the mirror and the difference huge. It's not perfect, but it's good enough for me as I did not want to poke around too much.
The mirror before cleaning:
The mirror after cleaning using the sensor cleaning kit:
---------- Post added 09-05-22 at 09:33 AM ----------
Then I went to disassemble the top so I could clean the focus screen. I managed to unscrew the rewind knob spanner using tweezers. For the spanner that is holding shutter speed dial I made myself a "tool" by nipping a part of a safety pin that I then held by a pair of pliers and unscrewed it.
Here's the "tool":
However, soon after removing the top I encountered the first problem. I removed the prism and there was a ton of foam that has disintegrated completely. Now I don't know what to do with that foam. Is it safe to remove the remains completely, or should I replace it with something? From
this post I get an impression that later Pentax cameras did not use this foam around prism anymore. However, I checked some K1000 repair videos on youtube at the foam was in all of them.
And here's the picture of that awful foam remains inside the camera: