Go to the nearest Consulate or if your Washington D.C., the Embassy.
You can find a consulate here:
http://ukinusa.fco.gov.uk/en/our-offices-in-the-us/contactus/nearest-consular-offices
NO.
A passport.
Yes, you can.
Your question does not make sense. You need to be a US citizen to have an American passport. If you have a green card and an expired Russian passport, contact a Russian embassy in the US and they should be able to issue you a travel letter or stamp your passport so you may travel back to Russia. But returning to the US is another problem.
No, you cannot leave the US with an expired passport.
You must always use a valid American passport when entering and departing the US even if you are a dual citizen.
I live in the USA with a Green Card but am a citizen of the UK and a UK Passport holder. I am thus to the USA/US Immigration a foreign passport holder.
No, you cannot travel inside the US with an expired passport.
No, you cannot travel within the US with an expired passport.
No, you cannot travel within the US with an expired passport.
Yes, have you applied to renew your expired US passport?
Yes, you can renew an expired US passport by submitting a renewal application form, your expired passport, a recent passport photo, and the required fee to the US Department of State.