Only if you're teaching in front of a screen, without any students physically present. That would be similar to teaching [any subject, such as English] online to students based outside of Thailand.
The DTV is better than a multiple entry tourist visa. I don't think anyone is really upset by a DTV. They're more likely to scrutinize certain people for having been on visa exempt or tourist visa entries.
Not closing balance every month, but every day...if you apply in KL or Laos, you can't allow the balance to go below 500,000 for 3 months in the case of Laos or 6 months in the case of Malaysia.
That $100 fee (roughly 1900 THB) is a tourism tax all foreigners on tourist visas pay when applying for a NZ tourist visa. Exemptions apply for Australian citizens and citizens of certain Pacific Island nations.