RE: I am searching for a plugin that show the members of our self emplyed community to the public, with a circled phote plus some introductions like Name, Place, Function, Website, Social links AND with a link (rather a pop up) with extra info about them
It does not show the website in the list view or use a popup to display additional details. It does show the website on the profile. The email and social media link are shown as icons under the photo.
RE: a search box so visitors can find them at their key words on front page as well as in the pop up or maybe a new memberwebpage.
The Circle template does support a keyword search field and can be enabled. This keyword search is placed above the direct on the same page.
If you would like to put a search field on other pages, the Widget Pack includes a search widget which can be placed in the theme’s sidebar.
Hope this helps!