Hello VidBat,
It sounds like the iPhone is having issues playing videos, along with some general performance problems. Let's check a couple things and see if it helps.
Start by power cycling the iPhone using these instructions: Restart your iPhone This can refresh the iOS, apps and connections.
Are the videos having the issue playing downloaded to the device, or are they stored on iCloud? Tap on Settings > [your name] > iCloud. If Photos is set to On, tap on it and check if Optimize iPhone Storage is enabled. If it is, then the high resolution version of the video is most likely being stored in iCloud, while a lower resolution version is kept on the iPhone. If you use a computer and navigate to iCloud.com and log in with the same Apple ID and password, are you able to play the video from there? If so, try downloading the video to a computer, then share the video with the iPhone and see if it is then able to play as expected.
Where these videos taken with this iPhone? If you take a new video, does it play as expected?
As for the other issues, tap on Settings > Battery > Battery Health. What is being shown for Maximum Capacity? If it is showing less than 80%, then the battery would be serviced. This could explain the issues you are seeing. iPhone Battery Replacement - Official Apple Support
We hope this helps.
Have a wonderful day!