Thailand is one of the few countries in the world that does not require your passport to be valid for 6 months in order to enter.
BUT the rule that Thailand goes by means you're still not allowed to enter. Because your passport must have enough time left for the stamp you will be entering on. A DTV gives 180 day stamp. So if your passport is not valid for 180 days then you're not eligible to enter Thailand. You'll either need to renew your passport in Indonesia or you'll need to return to your home country and renew it before returning to Thailand.
They don't care that you want to enter Thailand to renew your passport. That's your problem, not theirs. You're simply not eligible. Your airline won't even let you board your flight.
Most immigration offices in Thailand will not let you apply for an extension until you have 30 days or less left on your current permission to stay. A few allow 45 days or less, but 30 is the standard.
No, Thai languages doesn't qualify for DTV as it was not on the initial infographic that the MFA released about the visa.
For an ED visa, you must attend class in person. You're saying that you need a visa to be in Thailand. If you were taking online classes you wouldn't need to be in Thailand, you can do that from your own country, so you wouldn't need a visa.
That depends on your immigration office. Most allow when you have 30 days or less left. Some allow 45 days or less left, including the larger offices like Bangkok, Phuket and Chiang Mai.
She can travel on whatever passport she wants, but she should enter Thailand as a Thai citizen using her Thai passport.
If she enters Thailand using a foreign passport, then she is a foreigner as far as immigration law is concerned. The difference is that instead of the 30-day extension, she can apply for a 1-year Thai citizen extension.