At what age can a coach or a manager can manage a team and what is the minimum age required to be a coach in any of the following leagues?
In Germany (1. + 2. Bundesliga and 3. Liga) you are required to have a "Fussball-Lehrer" License, which also counts as UEFA Pro License. This license is required in order to coach a team in the top flight domestic leagues as well as in the European competitions.
There is no direct age restriction for the Pro License, but there is one in the lower tiers of the licenses and you are required to have several years of experience in order to get there. In Germany the way up is:
(C ->) B -> Elite Youth -> A -> Fussball-Lehrer (UEFA Pro)
(You can start with B directly, if you're qualified for it)
So at minimum you're 18 years old when starting with the course (when your B license experience gets credited to your A license, otherwise you'll be 19 years old). In Germany it'll last about 10 months, so you'll probably have to add another year to it before you can start working.