Does my application need to worry about setting timeouts on the REST API calls? If so, what is the Cisco recommended timeouts?
Yes, it is best if the application sets the timeout on the REST API because it not guaranteed that they will never time out.
In the Finesse out of the box UI, it uses Shindig which has a 5 second timeout for REST requests. For the notifications, the Finesse out of the box UI waits 10 seconds for the event before it times out and displays an error. So, those would be the recommendation.