How to weed out and correct corrupted video files?

Hello,

I am editing together a virtual choir project for a teacher friend. I am running into issues with a handful of the files that were uploaded by the students and all the beautiful headaches that come with a project like this.

I have a couple specific questions below in red.

Frame Rate issues

As is the case with most virtual choirs I've edited, the files have come in with all sorts of wacky framerates (29.96, 30.01, 51.38, etc.). I know there's not much we can do about that now short of having the students re-record, but nearly all of these were recorded on school-issued iPads--why the wacky framerates? That gives my computer a real workout when there are 40 videos currently playing on the timeline.  Am I correct in assuming that Modify > Interpret Footage will not work because that will also re-time the clip?

Corrupt files

I have identified a couple of the files that I'm assuming are corrupt because when they are added to the timeline, the audio plays, but the playhead freezes and and cannot get the audio to stop playing*. When I remove the files in question from the timeline and reboot Premiere, everything kicks back into working. But my quesion is: Is there a way to identify WHY a file is corrupt or how to fix it? Obviously I can't just discard the file as all the students need to be present in the final project.

A couple of the files also have extremely strange playback in Premiere. (They are .mov files recorded on an iPad.) On Google Drive (where the students uploaded), the videos play back fine. When downloaded to my computer and/or played in Premiere, they are extremely stuttery--looking like bad stop motion or something (Audio is fine). The downloaded file does play back smoothly/correctly on VLC player, but nothing else. Any idea what's going on here?

*Note: This is NOT an issue with needing to update my GPU driver. That is up-to-date.