Concerning Japan: I figured that since Russia picked away at Poland-Lithuania, Sweden, Turkey, Central Asia, China and pretty much all of its neighbors, why would it not do the same against Japan. Aside from the fact that it took a better part of the year to get a message across Siberia.
Well, in a sense they did with the Kuril Islands and Sakhalin, which the Japanese considered theirs just as much as the Russians did.
To address some other points:-
The Russian American Company would have established its interests in California at the time when it was a) Spanish and b) very sparsely settled, so it wopuld be the Spanish they would be dealing with, not the Mexicans
The bloke who was the power house of the Company died whilst on his way back (IIRC) from visiting the Tsar to get additional backing, and his death basically demised the company's long-term future. Had he lived...
Whilst the distances involved are huge, that in itself is not an unsolvable problem, since they were expected to be huge and people dealt with them.
Russia DOES have ports in the Far East, developing Petropavlosk in Kamchatka, and also smaller ones like Ayan in the Sea of Okhotsk. Obviously these freeze in Winter, but are usable at other times.
A lot of European navies developed the practice of keeping squadrons of their ships in third-party ports - see Chemulpo in Korea in 1904 when the Variag and Korietz were sunk, and look who else is in the harbour; Shanghai was also another popular base. The Italian and Austrian Pacific squadrons were ENTIRELY based in third-party ports.
Russia was quite happy to sail its fleet where-ever it was NEEDED - look at Seniavin in the Napoleonic Wars sailing the Baltic fleet into the Med and back again. The question is one of NEED, and of that need eclipsing other needs.
Best Regards
Grey Wolf