Pictures in jpeg format use EXIF to store metadata, in case you rename the file or change its timestamp is very useful. However, I don't know if that is the case for video files. Is there any kind of format that supports such implementation? The only way I know of preserving metadata on a video file is either set the filename correctly or use mkv with the description fields and such. However I would like to see if that can be done in mp4 of avi format to make it more widely playable.
Yes, but it differs by file format. For example, the QuickTime container format has many types of metadata within. This format type is used by MOV, M4V, MP4 and other less popular ones.
You mention MKV (Matroska) which uses a different container format again.