I would like to have a certain part of my store where only select customers, that have a password, could shop there. Is my 6.2pro version capable of doing that?

You can do this using customer groups if you are using cre b2b. You can assign cerain categories and/or products to certain levels of access.

There is nothing there for individual access though, if you were looking for that then you would need some modifications, but it is do-able.

Steve