Can a high school issue a transcript to a middle school student that shows the middle school student took an AP course at the high school?

Yes, high schools (grades 9–12) can use the AP designation for authorized courses and can indicate AP on transcripts for any student who took the course at the high school, including middle school students who attend the high school for the AP course.  Middle schools (grades 6–8) may not offer AP courses or issue transcripts with AP courses, with the exception of AP world language and culture courses that can be offered by middle schools for students in grade 8 only.