1. What is the health monitor doing when you leave the send string empty ? Is this simply a socket based check ? Which would give us not much more than a standard TCP monitor?
I've never tested it, but I don't see a reason to do this. I don't think an HTTP monitor could succeed without a send string. I assume bigd would establish a TCP connection and send no data.
2. What is the check for a success status when using the default “out-of-the-box” http health monitor ? (get /\r\n)Does it expect a HTTP 2xx return code?
If there isn't a receive string configured any data the server responds with will be considered a success. Again, I don't suggest doing this--you should always configure a receive string for an HTTP monitor.
SOL2167 is a good place to start for building HTTP/S monitors:
sol2167: Constructing HTTP requests for use with the HTTP or HTTPS application health monitor
http://support.f5.com/kb/en-us/solutions/public/2000/100/sol2167.html
Aaron