No, August is not too early. As long as you feel you are ready and you can find a testing seat, go for it.
SAT registration for August/September/October is now open to everyone, as the priority registration period for those rescheduling from the spring has now passed. Some places in New York are reportedly having an issue with all fall 2020 seats being full and students not being permitted to travel too far from their area to take the exam, but that isn’t happening everywhere.
Georgetown, Yale, and Carnegie Mellon were, I believe, among the few holdouts in terms of requiring you to submit all scores. Things are constantly changing these days, so do your own research.
Not a lot of colleges ask for the SAT essay. Again, you have to do your research to see what the colleges of interest to you require. DD was given the option, when we registered her, to keep my credit card number on file. Doing so in turn gives her the option to add the essay portion of the test at the last minute, which would give her more time to research what her colleges want, see how well she does on them in practice this summer, see how she feels at the end of a grueling hours-long test, and have more time to make that decision.