When connecting a group geometry inside a piece of geometry, there is an option to group by pattern and ‘transfer selection to pattern’. When I select some points and click on this button, the resulting pattern is ALL of the geometry's points, not my selection. What is wrong ?

I don't understand what's wrong either but here is a workaround:

Make your selection in the viewport and then press tab (in the viewport!) and select your group node. You will then get the selection as a group in the pattern entry.