Other than payslips you should get a letter from the company saying you have permission to work remotely from Thailand and that you won't work with any Thai entities or any clients inside Thailand
You can only apply using the Thai consulate where you are physically located. You can't pick and choose the consulate other than by travelling to the location of the consulate and then applying. You also have to remain in a location relevant to the consulate until the visa process completes
a covering letter explaining that should do most of the work for you, but if you can show money flow and tax returns so much the better. It's not necessary to have a business licence