The seats at my school are already full for the August one.
You can go to any school for the SAT, not just the one where you are enrolled. See if there is another school with openings within travel distance.
You will have to check with your colleges’ admissions departments for their last acceptable testing date.
You may need to take the test at another school. Look at College Board’s website though. I saw something recently that stated they will be processing tests much more quickly for some tests in the upcoming school year.
Yes. Per the new release schedule, the multiple choice scores will become available from October 20-26
With the new score report schedule this fall, it should be available in a couple weeks after the test. Nevertheless, there are recent cases that CB and ACT were holding up the scores for longer time than expected (like in May and June). So don’t count on it. You may look around for other test center within driving distance. My D2’s SAT2 test center in August is 30min driving away.
Most important, the score deadline policy varies from school to school. Some would accept it even a couple weeks after the application deadline. Others may require a previous score report to keep your application active while pending for new score.