PLANS FOR NEAR FUTURE aka vacations 
I hope I'll be able to make moves myself, but I'm far from certain. In case You play - I'd like You to know what my plans and thoughts are. Remember they are just plans, though, and are subject to change if threats or opportunities show up - if You strongly feel something else should be done, go for it (and leave me note in thread).
Military:
2 of our neighbors have more Power - I think investig some hammers in military may be wise

. I think we need ~4 Chariots for active defense, killing any threatening Barbarians and some scouting. We would also need defenders of 3rd city: Axe+Spear, I think. Of the above we already have only 2 Chariots (but would have another one in 2 turns, I hope). These are _necessary_ builds - if we have spare hammers for more, we can use them

. Also, 3rd city may get one of our Archer defenders, and new construction will protect Capital or Shanghai instead.
City production
Beijing: Library ASAP (the plan is to whip it), Settler to be ready when iron Working is in (to build 3rd city ASAP), some military in between (3rd city defenders/more chariots are both important).
Shanghai: Granary (with whip probably), Library, then - maybe Barracks to be able to produce trained military?
I think both cities should go lightly on whip (after Granary/Library, at least) - they have many good tiles to grow into, cottages to grow, one of them has Great Scientist to produce (Beijing probably). Academy should go to commerce city (hopefully 3rd, else Beijing).
3rd city: whip-heavy in the beginning to get out infrastructure
Worker actions
I marked 3 tiles as cottages (2 of them are ready) - I think that's enough for Beijing&Shanghai, they won't have population to work more any time soon anyway. That's already more than planned in the beginning

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Necessary infrastructure for Beijing is there, Shanghai has some resources still unimproved. Workers may improve further, build road network (priority after 3rd city site is chosen!), cut down forest to help (good for Settler, but may also be saved for Forges and/or some Wonder), build some mines.
Research
I think short-term path is pretty much set: Writing ASAP, then Iron Working. I haven't put much thought into what next, but probably some commerce enhancers: Mathematics->Currency (will open Calendar, too!), or maybe Monarchy (if so - maybe Monotheism first, for Organized Religion?)
EDIT: actually, Monotheism isn't very costly, and it gives 2 serious advantages: Organized Religion and Holy City status for 3rd city (which should settle any border disputes it might have)! So I think it's worth researching right after Iron Working, even if we don't go for Monarchy at first.
3rd city
I feel that 3rd city ASAP is important - and I think it should be commerce center (if Iron location allows).
I assume that if Iron is in undefendable location (or completely out of cultural borders) then new city should be near Iron.
If iron is not the deciding factor - for now jungle SW of Beijing seems the best. There is both Gold and Gems there, some food and some of farmable/cottageable land. That jungle needs to be scouted more once we have some healthy Chariot!!!
The best city site I see now is
1SW of Gold. It claims both Gold and Gems (and Spices to boot) and has plains hill for production (and overlaps Copper for even more production when it needs it really bad). Cons: only one food resource, and it's on Celtic Pride border.
City sites we don't see now will be on someone's border too, though
1SE of Gems may be good, too, if there is something great in the fog under that location - for now it loses Gold and most production, but takes safer food in 2 bananas and fresh water access, and more grass for farms/cottages. If it has something nice in the fog (resource? hill(s)? flood plains?) it may be even better site.
Big thanks for being there to make moves - I would have problem otherwise (and game would slow down)!