Currently there are no reports of that being checked on entry. They will check if you try and get an extension at your local immigration office inside Thailand
There is no grace period in this sense. If you spend 90 days inside Thailand you are legally obliged to make a 90 day report. The grace period only applies to reporting, not the requirement to report. So you can make the actual report in person from 14 days before through 7 days after
You don't need a visa of any kind for an online language school, just sign up and study online from your home country. If you want to study thai language inside Thailand then sign up with the school and get the paperwork from them to apply for an ED visa. For the DTV you need to be either a remote worker/digital nomad or apply for one of the approved soft power activities medical, cooking or Muay Thai having signed up with a facility that will provide proof of a bare minimum of 6 months activity preferably longer