Good up-to-date info, thanks!
I experienced the same many years ago - anyone can do the translation. Good to see that it is still that way.
One recommendation is ... if your WA is a full, unrestricted motorcycle endorsement, make sure your friend's translation includes a notation that you are licensed to ride BOTH 2 wheeled motorcycles and 3-wheeled sidecar motorcycles. In WA state, I believe, a sidecar license & a motorcycle license are the same thing. In China, they are different. In China, just a 2-wheeled motorcycle license is a C1E (C1 = passenger car and E = 2 wheel motorcycles), whereas a C1D includes passenger cars, 2 wheeled motorcycles, and 3 wheeled motorcycles (sidecars). You may as well shoot for the C1D, as you are indeed licensed for sidecars.
In my experience, the Beijing TMB are pretty good when dealing with foreigners. Given the large foreign population, with all of the Embassies, etc., they have pretty much seen it all and do not appear to have any concerns with foreigners becoming legal. In fact, the TMB actively encourages it. Seriously, there is no reason why anyone in Beijing should not be licensed.
As for bike nights, weekly rides, etc., I've recently been riding more outside of China than inside, sorry, so I'm a little out of the loop. There used to be a Tuesday night meet-up at Frost Burgers in Sanlitun, but I don't know if it is still going on. With such a transient population, it is really tough to organize and maintain anything. Frost is listed on The Beijinger, and you can contact Jeff (the owner, an American) for more info. Jeff is a local rider.
Finally, answering one of your initial questions - yes, a B plate is fine for anywhere outside the 4th Ring Road, except on the actual 4th or 5th ring road (side roads are fine). If you are in the NW (Haidan district), the rule may be that you still technically need an A plate to register the bike in your name. Haidan is one of the 6 restricted motorcycle plating districts. However, a decent motorcycle shop (pick one of the large ones) can help you out with how to get a B-plated bike.
Good luck in your pursuits!