For now, I suggest to use the TMS FNC Cloud Pack category for this.
Wrt the timeout, do you get a response from the server in other ways than REST Insight? If the server is causing a timeout, there is little we can about this from REST Insight
"The url as shown in the line at the left of send button seems to be OK and if I copy it to my browser it works."
Can you share this URL so we can test from here?
It is internal server, that is why I am writing about dns/proxy server.
Also, a usefull addition is to have a list of api calls with their data in tabs. usually we run calls in a batch