If I use EasyTool Professional to configure a system that includes a burglar alarm line and a home automation line (climate control, Event and Scenario management), can I do it without installing the control unit?

No, the control unit is necessary because the By-me system can't function without it. In the burglar alarm line, the control unit manages all the control and event logging functions, while for the home automation line, the control unit is essential for scheduling climate zones and events.