Yes, you can apply for German citizenship and be a dual citizen regardless of the fact if your mother was still a German citizen or not.
If you hold German citizenship, whether dual or not, then there are no occupancy requirements.
Contact the German embassy or consulate. Explain your situation and they will tell you whether you have lost your German citizenship or not and will tell you if you can regain it.
Yes. It depends on what you mean. You may or may not be German in heritage, but legally you are a German if you have German citizenship. All depends you could have a split nationality meaning you have a dual citizenship.
The child will have dual citizenship in Canada and America. It depends on why the couple was in Germany. If he was stationed there for military reasons, the child will have no type of German citizenship.
I don't know what New Zealand thinks about dual citizenship, but I added a link to the circumstances under which Germany allows dual citizenship.
The US recognizes dual citizenship.
India does not allow dual citizenship.
Yes, Thailand allows dual citizenship.
Yes, Venezuela allows dual citizenship.
Yes, Poland allows dual citizenship.
You may have dual citizenship, get in touch with the German Embassy and ask them. If you already own an American Passport that will be enough to visit other countries. If you decide to maintain dual citizenship, you could be called into the German Army for a 1 year assignment which is manditory.