German work Permit or work eligibility " Not Work Visa " Process Time

Hard to answer since your English is not correct. But of course one needs a work permit for a specific country. Having one in Belgium doesn't mean that one can work in Germany. And of course they want information about a spouse and any minor children since this is critical to get a family reunion visa if you intend for them to join you. This all seems more than obvious. And how long things takes is hard to say. What did the officials tell you or did you not bother to ask? And it is shortly before Christmas so if things are not approved before the holidays then expect it to take a few extra weeks.

Normally, the employee is himself responsible for applying for the required visa at the nearest German embassy.
Did you also sign an authorization with which they can apply on your behalf? If not, they can't.

Dear @TominStuttgart

Firstly Thanks a lot of your answer ,
I know that I need a work permit for germany , since I don't have a Blue Card , and my work permit is only for belgium
but what I want to know
- Regarding the german work permit , what is estimated process time
- Did I will need extra documents to be eligible residence in Germany

Dear Neppi ,
I guess I don't need a visa , where I'm already in the schengen area 
did I'm correct or wrong ?

My nickname is Beppi.
("Nepp" is a German colloquial word for rip-off!)

A Schengen visa allows you to visit (up to 90 days), NOT to live and work in Germany. Thus you do need another visa.