Elektron Websocket is a server-side API, it does mean that you can use any WebSocket client library which supported by the programming language you currently use connecting to the server. If the WebSocket library still supported on Windows 7 your application should be able to connect to the server.
If you running the WebSocket application in web browsers, it is not depending on the OS version (Windows 7, Windows 10 ,etc). It is based on whether that web browser supports WebSocket connection or not, which the older versions of IE do not support.
We need to use the Secure protocol only, does Elektron WebSocket API support wss connection? Does TREP perform wss for us or we need to set our own SSL accelerator? (from WebSocket API Webinar Nov 29)