If an application has already an opened WebSocket for live feeds, should I use it over AJAX for the other communications with the server?Because the connection is already opened, should we use it for requests that are Request/Response and not real time? I prefer RESTful HTTP requests because I find them more easy to debug. You can use a browser with urls or curls to test what the API returns. You don't have to write code to open a WebSocket.  Would it be weird to have RESTful HTTP API and a WebSocket in the same application? 
RESTful HTTP and websocket in the same application?
rest;ajax;websockets
One of the core design goals of Websockets is that it allows both HTTP and Websocket protocols to be communicated over the same port.  It achieves this by explicitly requiring a client to perform a Websocket handshake with an HTTP Upgrade request.  In this way the server can handle a standard HTTP request connection as well as an HTTP Upgrade request that is now upgraded to a persistent bi-directional duplex connection.So yes, this is definitely a valid use case, however whether you SHOULD do this for your specific application is a different matter entirely.  Websockets are useful and make sense where you have scenarios that the server must have the ability to send unsolicited data to the client (live feeds).  HTTP protocol and REST services are useful where you want blocking synchronous client solicitation of data.If your requirements are such that both of these make sense for your application then by all means you should use both.  If however your only interaction with the server is live feed based then REST services are not appropriate.  I think ease of debugging should rank rather low in importance in terms of System Quality Attributes that you should architect your design to.