@Frank-Steven **********
Take part in courses does not mean that in between periods of training you cannot do a job in another country.
There is no rule that you do the course 12 months a year during 5 years.
And income not comes always from work, there are other ways.
I know German people always want a strict rule for everything, but for some things it is just better to have general rules and let human beings fill in.
You will find especially concerning visa rules there is a lot of freedom in all countries.
A minimum set of rules is in law, the rest has to be done at descretion of people.
Visa processing is just not exact science.