Currently there are two python application demos provided (pull requests with demos in different languages welcome).
Since the server communicates with JSON all languages are supported. The API is language agnostic. Your web applications, crons, queues can communicate with it just fine.
This is deployment dependant and varies depending on what you are doing with the server, but biggest known deployment is around 600 concurrent connections and the server takes 100MB of ram and around 5% of a single core in this specific scenario.
Yes, 0.6.14 release is the one that supports both Python 2.x and 3.x - you can use it directly with python 2.7. However, since the server is standalone you can deploy latest version it in a Python 3.6 virtualenv which is the recommended approach.
Not out of the box currently but when the plugin API materializes this could be possible via separate plugins.
Solutions mentioned above are first and foremost chat services (you need to for example register accounts in Matrix). Channelstream aims to be general purpose real-time push server that tries to not get in your way.
You can model the data flow how you want, mix types of channels and messages as you see fit to meet your business goals, for example you can create an online game lobby and specific game channels for players to subscribe. It can be also (and there are few implementations) used do develop real time chats but this is just one of it's many uses.