if you can apply for German passport or not, depends on your previous status: if you have a residence permit the whole time or only a part of this time (for example you had Duldung or were in the asylum procedure). You must have your residence normally for at least 8 years, in some cases less.
If you have money from Jobcenter, it is ALG 2. But perhaps you get it only as additional paying for children.
If you did und do everything possible for your integration in the job market in Germany and it is not up to you that you can't earn the living for the whole family, it can be possible to apply for citizenship. If you make Ausbildung in the time of your application, the money from Jobcenter for children must not be a problem, this situation makes one of the exclusions from a general rule.
German language can be a problem. You must have at least B1 in oral speech and writing.
Have you already spoken to the Einbürgerungsbehörde? It is the authority which deals with the applications for a citizenship. I strongly recommend you to make an appointment there and also look for a good migration consultancy in your area.