Yes, can confirm. You can start a GmbH with exactly half of it (12.500€). And the money does NOT need to stay locked on the bank account. You can spend it for company purposes (but NOT for founder wages).

Founder wage is a company purpose, else it wouldn't be allowed. Its not your personal money anymore once deposited into the companies account.

Yes, afaik you can pay out founder wages with Stammkapital.

However, it has to be actual wages, i.e., the founder has to do work in return for a salary, and the salary has to be reasonable. You can't just have the GmbH pay you back the money you put into the company. There are also other limitations (https://dejure.org/gesetze/GmbHG/30.html), but that's the main one.

The difference is shareholder (=Gesellschafter) and ceo (=Geschäftführer). They may be the same person. So paying wages for the work as Geschäftsführer is fine (reasonable amount, taxes, etc), paying out money for being a Gesellschafter is not.