You travel outside of Thailand to the location of the consulate you wish to use, apply there and remain there until the process completes. You can't apply from inside Thailand
As of what date did/will you stop working? That is the date your extension of stay becomes invalid and the date you must leave Thailand. You must cancel both before leaving. As said above you are on a Non-B not a Non-O, the only way you can work as a teacher on a Non-O is if you were married to a Thai.
Anonymous participant there is such a rule but usually it requires that you either interact with Thai entities or clients inside Thailand. The DTV expressly says you can do neither of those things. For more information check the DTA between your country and Thailand
Anonymous participant I don't think you need to do that, particularly if the company you work for has no presence in Thailand. Just apply as a remote worker with permission to work remotely from Thailand doesn't impinge on the company in the slightest
If its your parents providing the finance they should be able to provide a sponsorship letter but they may also need to show the money in their account
but that's irrelevant. The question was if someone working remotely for a foreign company created a de facto thai entity. It doesn't. The companies you refer to already have a Thai entity