Is there something like EXIF for video?

Yes, I have used exiftool to read the metadata from mov videos from iphone and mp4 videos from android. It contains metadata like the datetime that the video was taken (not when the file was saved or modified). You can also use exiftool to write metadata as well.

https://en.wikipedia.org/wiki/ExifTool

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.

• https://en.wikipedia.org/wiki/QuickTime_File_Format
• https://developer.apple.com/library/mac/documentation/QuickTime/QTFF/QTFFPreface/qtffPreface.html

You mention MKV (Matroska) which uses a different container format again.

• https://en.wikipedia.org/wiki/Matroska
• https://www.matroska.org/technical/specs/index.html