The tool to see traffic is tcpdump. It's basically a command line sniffer that is on the LTM.
The following is a link to the TCPDUMP information on the ask.f5.com support site
(Click here)
As for seeing a persist stats you should be able to within the GUI statistics and select persistence records.
If you are looking for the actual records then go into the CLI and use the following command
bigpipe persist help
This will output the commands you might need to spell out all the persistence record for the specific virtual server.
Hope this helps,
CB