I'm trying to understand where I can configure a request timeout for all requests arriving to a servlet of mine (or all of my servlets)? Is that, as I think, a container property? Also, how does this affect different browsers? Do they all comply to the parameter the container dictates? Or maybe the request timeout time isn't even something I can control and each browser decides on this on its own? (Just to be clear I'm not talking about session timeout)
The timeout from a client (i.e. how long it waits for a response to an HTTP request) is determined at the client. For IE, see this, and for Firefox see this.
You can't control this timeout from the server.