This is very unusual. The only program setting remotely related to what you describe is "Lock workstation on disconnect" property (connection properties -> additional properties).
But since you say that locking happens on connect rather than on disconnect, and that it is really Remote Utilities' own Full Control mode rather than the RDP, we don't really know what might the reason. This is the first time we are reported such behavior.
One possible explanation could be that there is security software on your computer that prevents remote connection and/or input emulation typical for remote control software.
The license count limitation applies to all records across all your address books. For the free license this limitation is 10. You can create as many address books and put as many records in an address books as you wish so long as it respects the total limitation.
You should try uninstalling the Remote Utilities monitor driver. Perhaps, it was installed on your Hosts. To uninstall it, right click on the Host icon, select Settings for Host -> Options -> Driver and click "Uninstall" right next to the monitor driver.