Can I use a TR visa to re-enter Thailand after my ED visa expires, and how many times can I apply for an ED visa?

Ask your school

It all depends if you're doing it legitimately and what you're studying.

If you're not doing it legitimately, I.e using an agent. Depends on the agent and how much cash you have... Most things are possible with an agent.

However, something you should always remember especially when using an agent

... just because it's possible doesn't mean it's legal, and you not the agent will be the one drawing the short straw every time if an issue should ever arise.

Have you considered the new 5 year multiple entry DTV visa?? If you want to learn the language, just sign up for some online classes, and get a DTV visa, if you are under 50 years old, you don't have that many options, apart from the Thai privilege visa (elite) which is very expensive, or you could get married to a Thai national 😅😉

I doubt you will be able to get an ED visa to study online any longer. But assuming you get to enter ok then you should be able to sign up with a school where you physically attend lessons.

Yes, you can apply again and pick up from where you left. If you change schools make sure you have the transcripts from the older one. This is what they told me at one of the better schools in Bangkok when I returned to the country and asked them if I can get another ED visa