Hi, I do administrate several PeopleSoft applications so I may be able to help you ...
Regarding the cookie persistance, it's mandatory that you enable the "oneconnect" feature on your virtual server, otherwise you could observe some issues with visitors switching their session ...
If you want to use https between client and load-balancer, then http between load balancer and web servers (weblogic or Apache proxypassing to weblogic), on the F5 you must enable the "redirectrewrite" feature of the http profile ; and you must also configure PeopleSoft to force https (peopletools > webprofile > webprofile configuration) otherwise the urls within the application will be http:// instead of https://
hope this will help