After properly measuring fret level and nut height, I've came to conclusion that I have uneven frets AND incorrect E and A strings height at nut. I decided to level and crown frets myself, so I've read a ton of articles on how to do that.
Here is what I needed, bought and used for this procedure :
1) level (medium-sized, cost me about 5 $)
2) sanding paper (240, 320, 1000, 2500 grit, about 3$)
3) sanding paper holder (something like rubber brick with flat bottom, about 4$)
4) black permanent marker ( 1.5 $)
5) paper tape (to cover the fretboard, 1 $)
6) various sponges with sanding paper of different grit glued to them (turned out invaluable thing! , 2 $)
7) superglue, 0.5 $
8) linen oil (small bucket, like 6$, hope to use for next 30 years or so, with such quantity

)
Leveling and crowning turned out to be fairly easy, but time-consuming process, also you have to be careful to not screw things up, so I've double-checked everything that I was doing.
1) removed strings from bass, unscrewed neck from guitar
body, placed on even surface and fastened it.
2) covered fretboard with paper tape, leaving frets intact.
3) marked all frets with marker.
4) using 1000 grit sandpaper on a sandpaper holder, I've lightly sanded the frets all over fretboard, till marker disappeared. Turned out that frets were fairly even (though needed some work) starting from 24-th to 7-th fret, but having like "bump" at 5-th till 1-st (thus explaining that pesky rattle of E and A strings). All of them were firmly sitting in fret slots (so, no superglue was needed)
5) marked all frets with marker again, I've started sanding down the frets with 240 grit sandpaper, then with 320 grit,checking with level. that took me a while.
6) leveling was done, time for crowning. marked all frets, and started sanding each with sponge to get that half-round shape, gradually going from lowest to highest grit. level checks were handy.
7) with 1000 grit sandpaper between 2 fingers, I've lightly went along the fretboard, polishing frets, same thing with 2500. that took a while too.
8) removed paper tape, sanded back of the neck with 1000 grit sandpaper to get it smoother (turned out very useful, neck is much more "faster" now), cleaned fretboard with whitespirit (careful not to spill on laquer finish of the neck)
and applied 2 layers of linen oil on the fretboard. left it for 8 hours to dry.
9) screwed neck back to body, strung it and adjusted action, lowered it about 1.5 mm lower than before, no buzz at all! (still I have like quite high clearance at 17-th fret, but I think I can get it to 2 mm, even with such improper nut!.
Overall, I'm really happy with a result. Im no woodworker by all means, but it turned out fairly easy (thanks Internet

) Next step would be replacing the nut.
Pics will follow later.
