I would like it if the items already selected were then not shown in the lookup, so if I have already chosen an item then it shouldn't be shown as available still.
Are you referring to the case when you are changing an existing value and the menu shows all possible? In the described scenario you'd like the currently-set value to be omitted?
Not just Editing, also adding.
So I am creating a record and the Connection Field has 10 options/choices, as I pick option/choice 1 so it is now really taken from the "Available" and added to the "Selected" so it shouldn't then still show in the Connection Field (Available) when I start to type again as I can't/don't want to add it multiple times.