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Also: nomads don't declare wars if they're experiencing Tribal Succession Crisis. Not very useful as you can't plan that but good to know.
 
Is there a way to check which group is in control in Ming from the outside, that is, while playing a different nation?

No, because the AI isn't burdened with the factions. It plays Ming just like any other country.
 
Does culture or religion ever change on its own simply by being non-accepted? Or does it have to be manually changed through settlement policies and missionaries? Playing as Russia I'm wondering if I'm going to have to manually convert the entire GH...

Edit: What is the auto-white peace function I've been hearing about?
 
Does culture or religion ever change on its own simply by being non-accepted? Or does it have to be manually changed through settlement policies and missionaries? Playing as Russia I'm wondering if I'm going to have to manually convert the entire GH...
Culture yes, religion no. You'll have to change it using missionaries. There are a few requisites for the event which changes cultures in provinces: http://www.paradoxian.org/eu3wiki/Cultural_Assimilation
I don't know what main culture Russia and Golden Horde are, but they may be hit by that -90% MTTH modifier.
 
I was defending.

The only thing I can think of is the fact that my current ruler has a military skill of 3. But I can't believe it would make me lose battles when I outnumber my opponents by that much with superior troops. I really have no idea what to do with this. Ottomans are scary enough as they are, but now even when I have 3 times the troops I still lose.

Do they have a general with 5/6 shock and fire values? That could account for it. Some generals are unbeatable.
 
What raises a province's production of a material? base tax? population?

Produciton : Price of good, and it's unit number, manufactories and high productiveness increase production.
Base tax - only events, but taxes are base taxes + bonus values. Some buildings increase taxes, some decisions too, and also events. Also bureaucracy national idea increase taxes by 5% and 10% if you play DW.
Population is raised by some buildings, manufactories for instance. Province being capital increase it, COT value also increase it(your province need to be COT to get it). Also province having high tolerance to religion in province increase it - low decrease it.
 
Do they have a general with 5/6 shock and fire values? That could account for it. Some generals are unbeatable.

You can see their general in the screen shot, 3 shock and 3 fire. I pretty much gave up on this, I waited them out and just settled for white peace. I guess I'll have to wait until I westernize my troops and then come back.