Customer User can add new Projects - How to realize

how can i set a customer User as an external Project leader to set new Projects on this Working Environment for himself

Just give habilitation to Project as for Project Leader. The users with the profile will be able to create project, with autoatic affectation to these projects, and will only see projects they are affected to.

add a defined internal Project Team to handle it

This is a bit more complex, as access to Resource is no/read/write, but without restriction to environment. If he can create resources, he'll be able to see yours.
What you can do is :
- define team yourself
- define top project for him, and affect him to the project
- affect his resource to top project
Then, when he creates a new project, he will have to move it under the top project (define new as sub-project of top) to be able to use his resources.

is it also possible, that one external project leader can have a look on all projects which are added to a special customer

Not this way, as there is no access right defined upon Customer. But you'll just have to affect him to these projects in order to give him visibility (and you can choose to affect him with a profile that will give him only visibility, and no update right)

additionally, how can i define, that some information in this project is just viewable by internal operators (such as special information which has to be handled and communicated "with respect" to the customer/external project leader

This can be done only for Cost ar Work, and is defined for each profile in "Specific access rights"

now the Customer wants us also to add a small Shop in - how can i define that he can add this as a Subproject and how can i add the possibility to let him add Documents and Activities..

I thing it is a very bad idea to let the customer create a project (even if it is a subproject).
I thing the best way is to let him create a request as a ticket : he will describe the need in the ticket.
Then, you'll be able to copy the ticket into a project.

To allow your ezxternal project leader, you must give the profile rights to create projects.
For instance in screen "access mode to data" give him Manager acces mode.
But he will then be able to create a projet than will possibly not be a sub-project, as "is sub-project of" is not mandatory.
Fortunately, if he wishes to set this new project as subproject, he will be able to select top project only amongst project he is affected to.