Yes, that is possible.
So any requirements are there? do I need to fill anything?
And how officials in Germany follows/check people if they are quarantining or not? Specially for children under 12 Years is there something like a mobile app or something?
No requirements and no form for people who leave the country straight away.
I thought you weren‘t going to stay in Germany so I don‘t quite understand your question regarding quarantine.
It‘s illegal to break quarantine and violators will be fined and in severe cases criminally prosecuted, that‘s it. The authorities may contact individuals in quarantine to verify their whereabouts but they won‘t monitor your phone or anything, that‘s likely illegal or even unconstitutional in Germany.
If you are bringing a child from a high risk area to Germany you will need to make sure that child stays in quarantine for 5 days.
I do not want to do anything illegal that's why I am asking how they are checking and want to make sure I follow every rule, currently I am bit confused on how the quarantine works if every person got to choose where to stay and nobody checks if you are actually quarantining or not.