How do I prevent clients to book whenever they want or during events that I have in other calendars?

The way the Console calendar works is that your entire calendar is by default "not available" to your clients/prospects. Unless you schedule available times on your coach end for people to book, they will not see any scheduling options when they go to your calendar page. So, if you do not want people to schedule, then you don't actually need to take any special measures about it.

Also, if at certain times you have other appointments in an external calendar, then all you need to do in the Console calendar to avoid double booking is to simply not schedule available times for clients during those events in your external calendar(s).

In the case of a 2-way sync with Google, you can also mark the events in the Google calendar(s) as busy on the Console end (in CALENDAR > Calendar Settings) so that, even if you happen to have some available times scheduled in the Console during Google events, these times will not show from the perspective of your Console clients as available options for booking.