Absolutely not most. What country in Europe has a significant amount of ambassadors that are not career diplomats / government workers ?
In France, Germany, Switzerland you would either need to be a career diplomat/ foreign service worker or in rare cases you would be a career government employee assigned as diplomat to some specific country for some reason (i.e you were trade minister and become ambassador to your biggest trading partner).
The most "political" appointee ambassador in Europe I can think of is Mandelson but he is (as we found out) supremely connected to US power networks and he is still a lifetime politician/ government employee.
It‘s not uncommon, though I‘d say even the „cool posts“ like Paris or London usually go to career diplomats.
The first might have joined the Foreign Service and worked their way up; the second might have had a career elsewhere (not necessarily in political office), get invited to work for an administration, and then leave once there's a change in power.
Parent is correct. The amount varies from administration to administration. But if you really want to be an ambassador, you're well positioned if you bundle a few hundred thousand to a few million dollars for the winning campaign. (There are traditionally limits. You can't usually buy your way into the U.S. Embassy in Baghdad or London. But for the postings with limited security implications, where the focus is on trade, you're mostly hosting expensive parties for your post.)
It is not. The vast majority of the world has a professionalized diplomatic corps roughly modeled on a Prussian or French system. As Fukuyama points out in Political Order and Political Decay the US is an odd case because it democratized before it developed an administrative state and as a result is somewhere between "Greece and Prussia" and ended up with a spoils-based and clientelist system, somewhat moderated by the Progressive era.