1) If a public viewer clicks on a Groupjive link in the CB Activity stream he is redirected to the default Joomla login form. However this form is not published. How can I make sure that he is redirected to the login form of CB?

CB does not redirect to Joomla login. It will always send to CB login or registration as needed. If it's trying to send to Joomla login then something installed is interrupting CB and trying to send them there. This is typically a Joomla menu item access permission error. You can prevent access to Joomla user component by ensuring our system plugin within Extensions > Plugin Manager is public and published and that Redirect and Rewrite or URLs is enabled within its parameters.

2) I would like to show groups and categories to the public but I do not want them to see items like foto's and video's and messages on the "wall". Basically I only want to show a group/category and if they click on one of them they are also redirected to the login form of CB. How can I accomplish that?

Set the groups to all be publicly accessible, but set the individual integration tabs as Group Users only. You can set the defaults for those parameters within GJ > Configuration. For existing groups you'll need to edit them to make the change. It won't redirect them though if the group is public and instead will just show them the group and display whatever information is public.