Can you apply for a DTV visa while in Thailand and when does it expire?

If you use a good agency you can apply online (evisa) while in Thailand. That's what I did and got it approved in around 5 days once I collated all the required documents. I just need to leave and come back to start it which I am doing in 2 weeks. Visa 10k baht. Agency fee 20k. Still crazy-cheap even with the fee.

You can't apply while inside Thailand

Correct in both accounts. Cannot apply in Thailand and it is for 5 years from date of issue4

Yes, you have to apply in another country. One of the requirements is that you prove that you are in the country where you applied for the visa. (photo of the visa in the passport) And the visa is valid for 5 years from the date of issuance.