Bulk cutting and compression
You would use FFmpeg for that.
It requires that you are a bit familiar with using command line applications but even if you are not its really not complicated.

The things you want to do have been covered in these questions (and probably others):
Why does quality degrade so much if just cutting video with ffmpeg? (different topic but the answer tells you exactly the two ways to cut in ffmpeg, the re-encoding one is the one you want).

Add an image in front of video using ffmpeg (watermark)

What you want to do is make 5 separate ffmpeg commands, 4 for your 5 minutes segments and one for your complete video.
Put those into a batch/shell/apple script depending on your OS and loop over your files replacing the input file name for each command set iteration.