Choose your DTV scheme and nearby embassy wisely for fast approvals and ensure you submit all required documents when you initially send them, including all pages of your passport.
No need unless buying an in country extension. That said, you should prepare yourself for possible questions upon re-entry, do not say your course is finished, state you are a remote worker and possibly prepare some portfolio of work contract proof etc. You have the visa and it's good for 5 years.
If you make a final entry into Thailand very close to, or on the day the visa expires you'll be stamped in for another 60 days and with an extension in country you can get almost 9 months out of this visa.