monterey 12.6, in photos, videos will not run

Do you have anything installed like extra video codecs on system preferences? 12.6 quicktime videos taken with a Nikon D80 work in Photos just fine.

Extensions such as Perian and Flip4Mac, may not work very well with newer OSes unless they themselves are updated for the OS and cause trouble for software trying to decode video.

But your other problems indicate that there something not quite right, so it is still a good idea to post that Etrecheck report.

Etrecheck is a diagnostic utility by a respected member of this community, and its report will let us know about possible software conflicts, which are causing the difficulties you are facing.

Videos not running may be due to what a brody said.

Applications not starting? Which ones? If you have just upgraded and have older applications from 10.14 Mojave days or earlier, they may be 32-bit and will not work on any OS since Catalina. Please clarify.

For more information, Please run Etrecheck and post its full report here. Use the "additional text" button and paste the report into the text box.

Image Capture is another good way to downloads the videos with the photos from the phone. Then open them with the Photos app from the Finder.

You will need to use a cable to hook the Mac to the phone.

Image Capture is already there in your Applications folder.

You can also reach it by pressing Command-Space to start Spotlight, and just start typing its name, and press enter (of course is also valid for other things in your mac).