How to view log Self service on a local macbook

In Console Application:

in the left column locate and down click: /var/log
then locate the jamf.log

you will need to be logged in as admin to view this log

While there is a Self Service log stored on every Mac that has run it (in the user's /Library/Logs/ folder) its not going to help you at all in determining why a package won't display to a user or Mac. You need to check all the settings in the policy on the JSS. Usually it has something to do with scope when a policy doesn't show up on an endpoint inside SS.
If you don't have access to the policy settings, I'm not sure how you'd be able to figure out what's wrong truthfully.

Who, or what, creates the Self Service policies for you?

The jamf.log will only show policies that have run and some/any errors, though not nearly as much as the actual policy log on the JSS. If something isn't appearing inside Self Service, which is how I read the post, there is nothing I know of on the local Mac that will help determine why. All Self Service does is load a dynamically generated webpage from the JSS. As for what should appear there, that all gets controlled on the JSS end, based on scope, smart groups, last inventory update, etc.