> As far as the "how" part, the answer depends on how much you know about django/python/web-development
That's my take on it as well.
They'd probably want to just be writing the frontend/content presentation and management components with Django & your choice of JS framework with a separate, dedicated video streaming backend for handling streaming efficiently. I've used red5 for random things in the past (I don't like it much, but it had a decent set of features), plus a quick google showed up a few more contenders in the space which may be suitable, depending on your specific requirements.
If you insist on using Django for the actual streaming component, Django supports generators in callbacks for streaming data, you can use Channels or go all-in and handroll something around Twisted or Tornado. This will be an educational experience. If you want something that just works, I'd recommend sticking with a dedicated, supported backend rather than hand-rolling.
This isn't a small project to take on or simple question to answer if you're looking at something on the scale of Opencast, but if you want to slap together a quick and easy frontend for people to use, some management around a few VLC processes feeding live stream sources into a dedicated streaming backend like MistServer appears to be (never used it - just came up in the search), then Django can provide some value.
As for PHP vs Python+Django, language choice is largely irrelevant and entirely up to what you're comfortable with. I'm biased towards Python, but IMO trying to write glue code between frontends and backends in PHP is a tragic mess. The popular backends in this space all seem to be written in Java or C/C++.
Personally I would recommend using Open Broadcaster Software https://obsproject.com/ from the streaming end and Red5 media server at the broadcasting end http://red5.org/
We did a 2 club event where 1 stage in each club was a live dj and the 2nd stage was the dj from the other club streamed live. It worked out pretty well in the end. This setup will take some more time and is a bit more complex that other options but it should give you the best quality and lowest latency possible w/ no 3rd parties in the middle