Hello and welcome back to the Wefugees Community,
I am trying to answer your questions as good as possible based on the information you provide. I don't know which residence permit you are holding. However, since you are living and working in Germany for more than six years, the chance is high that you are also able to apply for family allowances (as "Elterngeld" and "Kindergeld"). This is, because if you are not recognized as refugee or having the "Subsidiary Protection" but hold a residence permit like the one according to section 25 (3) or the 25 (5) of the German Residence Act, you are entitled to receive family allowances only when you work or stayed in Germany for more than 15 months (as far as I know).
Regarding your question 1: Yes, in general, you can apply for it also if your partner is not meeting the requirements (i.e. holding a "Duldung") or if you are the only one applying as long as you are the one officially doing it in your name.
Regarding your question 2: If you apply for the extension of your residence permit early enough and hold a fictional certificate ("Fiktionsbescheinigung") according to section 81 (4) German Residence Act in the meantime, you continue to be entitled to receive family allowances. With a fictional certificate according to section 81 (3) of the German Residence Act (either a so-called "Erlaubnisfiktion" or "Duldungsfiktion") you wouldn't be entitled.
Regarding your question 3: Unfortunately, I am not familar with the Croatian social security system and the rules to receive allowances/support. However, I advise you when applying for support in Croatia never to hide that you are already receiving support for the child in Germany and vice versa in order to prevent complications.
In case your application will be denied by the German authorities, I would recommend you to contact a counselling office as soon as possible to potentially get some support in contesting the decision on time.
I hope this helps and please don't hesitate to get back to us with any further questions.
All the best,