Does every country have obvious national borders that you can see when you arrive, or be stopped by the police... I'm worried that I might accidentally cross into another country while driving...haha ?

There are boundary stones, but they are generally not noticeable as you pass by, and then you will find that the language on the road signs has changed. If you are concerned about Switzerland, there are very obvious checkpoints between Switzerland and other countries, because Switzerland is not part of the EU.

There are no border controls between Schengen Area countries, and people and vehicles can travel freely. However, due to vehicle insurance issues, when crossing Schengen countries, you also need to inform the car rental company. Insurance policies for crossing different Schengen countries require payment, and the countries that require payment should be a minority. Switzerland is in the Schengen Area, but there are police at many borders, but crossing with a Schengen visa poses no problem.