Recently I disassembled, cleaned and greased Nexus 7 hub. After riding I noticed that 1,2 gears not engaging, 3 sometimes works and 7 gear feels more like 5. Not sure what's wrong, I have suspicion about pawls in one part facing in two directions and actually gears on right side from coaster brake are not rotating, here's photo. I used graphite grease, can it's thickness be problem?

If you used grease anywhere except the two weight supporting bearings, then yes, is might be the main problem.

My AW3 , I use oil on the innards and Grease on the axle Bearings.

I might try removing excess of grease but not sure how it causes problem. What parts are responsible who gears that are not working now?

Your photo appears to have been deleted, but if it's a coaster brake hub, it will have pawls facing both ways, so that's normal.

Dan B. is my go to guy on IGH hubs. He services these routinely whereas these days I do one once in a blue moon (if that often).

So he may be able to offer a diagnosis based on the pairs of gears lost, but I'm not.

OTOH grease on then internals can cause all sorts of issues, and complicate or mask any other causes. So I pointed out one issue, which may or may not be "THE" issue, or there may be other issues, but a proper approach is to address known causes before exploring possible unknown causes.

Look up some of Dan's videos and do a degrease and oil dip, then reassemble and see what you have (or don't).

I appreciate that, but my own education on gearhubs is far from complete. The 7 speed Nexus, while I have serviced some of them to the extent of partial dis assembly, cleaning and lubrication, I have not yet had the opportunity to do a complete study on power flow and engagement as I have on the 8 speed and other models. I do have a total understanding of the 8 speed design, but the 7 speed is somewhat different, most notably because there is no direct gear.
I hope to get to that one day, but it takes time, which these days is a precious commodity.
all that to say I don't really have an answer in this case.

Trouble Shooting 101: Try the easy stuff first.

Clean out the grease, oil the gears, and give it a ride...

I fixed that problem, probably something wrong was with core shifting mechanism. Still I feel little speed difference in gear 6 and 7, also 1-2 but maybe that's normal.
Other problem I noticed that there is somekind chirp sound in hub when pedaling, especially on lower gears. Maybe it's a problem with worn bearing cup and cone as ball bearings are loose?