Batch video editing software that can trim without re-encoding What application is there that can open a video, modify it, and save it?
(the software that I am using now, only allows the video to be used as a source, and then exported)

I have adobe premier, but it does not actually edit videos, you have to make a new project, and set the output type/settings, then import the video, then bring in the video, edit it, and then save it.

I also have iMovie, and again, project, import, edit, export.

Is there any application that I can open a mp4 video make edits (clipping segments) and save it in the same format/size/container/etc as it was opened in?
If you can script yourself, all you need to do is call FFmpeg repeatedly:

ffmpeg -ss [start-time] -i input.mp4 -c copy -t [clip-time] output.mp4


Here, start and clip times can be in the form HH:MM:SS.mmmm, or just in seconds. 



To give you a rough idea how that'd look like in Ruby, see this Gist of mine. It contains a script that takes an edit list, a folder of videos, and cuts them accordingly. I've used it very often for cutting videos based on an input edit list.

The edit list would look like that, with the timestamps in the proper FFmpeg format (e.g. 00:00:24.240) and the difference passed to -t in the last column.



Note that you can't expect it to work with any input/output without synchronization issues. If that's the case, you need to re-encode video and audio parts. I wouldn't use that script of mine though as it's not very … eloquent in that regard. Rather cut your video in a NLE.