Managing servers timeouts through iRules

This again depends on what the error is.

If the server is actually responding, but it's an error response (ie. 40x or 50x), then you can pretty easily trap that in an HTTP_RESPONSE event and modify the response to the user, or adjust your HTTP monitor(s) to catch these types of responses.

If the server is just down, and it doesn't respond at all, then hopefully the monitor would have already taken this guy out of the pool. If you're worried about it dying mid-session, then you can potentially look at timing responses or using an inband monitor.