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Regarding your current questions :
1/ The default for an icmp probe is 120sec, 3 retries and 300sec for failed.
You can use whatever values you think is necessary for your environment.
However, you need to remember that a probe generates traffic and each probe require process CPU time to send and receive.
With a lot of servers you probably want to avoid low frequency values.
I think your suggested value of 1 minute is ok.
2/ the sitcky timeout does not affect failover.
However, you should be aware that if a server goes dowm, the CSM will send NEW connections to the other servers. But active connection will stay with this server even if down. To change this behavior use the 'failaction purge' command.
3/ A connection is a flow. It is defined by a SRC IP, DST IP, protocol, SRC PORT, DST PORT.
Within a connection you can send 2 bytes or 2 Gig.
So, it is difficult to link the 2 values.
ie: when you load a webpage, if you are using http 1.0 you open 1 connection for every object (text, gif, banner, ...) but with http 1.1 you can download all the same objects in a single connection.
Hope this helps.
Gilles.