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.