For the transcript question, you would need to talk to the administration at your school. My D is taking (hopefully) the fast-paced high school physics class at CTY this summer and we needed the OK from the principal to enroll in AP Physics C for the fall.
We didn’t bother trying to get it on a transcript because we will have the CTY transcript. But they are an accredited school, provide the full syllabus, experience-based advice on how to work with school to get what’s needed, and will provide a grade if requested.
Their advice may be useful, wherever you decide to go - https://cty.jhu.edu/summer/about/credit.html - especially the linked Parent’s Guide pdf.