MPEG1 is a pretty old encoding and to stream (and I'm taking your word it must stream) the video and audio content must all be together inside a small space. If the mpeg1 file is not consecutive and the audio packets are too far apart or segmented it might not "stream." So while it is possible, did you really want to take courses and read books about all this?
And finally, you may have to buckle a little and try Chrome as a short term solution. Your post has good questions but most of it seems to scream why and tell me you are just starting your work in this area. Sorry but I can't condense all that would be needed in this small space except to write it's the wrong encoding for reliable streaming. Too old.
First, I'm a Mac-nitwit but the following has been dropped on my doorstep:
The company where I work has a lot of MPEG1 files and our customers stream these. Part of our customers use Mac-computers and different browsers. The website uses VLC-Player to stream the video. This doesn't work on newer versions of OSX and / or browsers.
What is the alternative? Various sources reported "NONE".
I found that curious so I checked the QuickTime specs and they stated that mpeg1 streaming is possible. In a quick trial it seemed that QuickTime is first downloading the file before playing it, so it's not really streaming.
So my question is: Is there a (short term) alternative to stream mpeg1 on a Mac, preferably on most common browsers. And yes, we are planning to transcode to another format but that takes time.