Can I apply for my DTV visa right after returning to my home country in late July, or do I need to wait until my ED visa expires?

I am in the same situation.

You need to cancel your visa/extension. For this, take a letter of cancellation from your school, go to Immigration and they will put a cancellation stamp in your passport with the date when you absolutely have to leave Thailand (the date in the school’s letter). This is free of charge.

You can leave earlier than that date but not later. After that date, you are free to apply for DTV as soon as you would like.

You need to cancel ED visa before leaving, atleast I had to.

If you leave without a re-entry permit is your ED not automatically cancelled or is that just for "B" and "O"?

Depends. Are you on an actual visa or an extension of stay? Check your passport. If you are on an extension of stay you need to cancel it, but can do so after you return. If you are on a visa without a re-entry permit you don't need to do anything