Hello @Faga0206
It is not clear what you mean in your second question regarding the judge saying that you as parents can benefit him. You son is initially entitled to a Duldung due to you being here and can continue receiving benefits from Sozialamt. When you have been issued with the decision on the national deportation ban, you can then apply for a residence permit for him according to paragraph 32, section 4 of the immigration law:
https://***-gesetze--im--internet-de.translate.goog/aufenthg_2004/__32.html?_x_tr_sl=de&_x_tr_tl=en&_x_tr_hl=en&_x_tr_pto=wapp
For him to get this, the authorities have to consider it necessary in order to avoid a particular hardship. In general, such a permit (unlike the ones the rest of you will receive) requires that your son is financially supported without accessing social welfare benefits. However, it is possible that due to the unusual nature of your case that an exception would be made.
With a residence permit for deportation ban, you are obliged to have passports. From what you write, you no longer have an ongoing asylum case and so it is required of you to have a valid passport.
The grey passport is a special type of passport for foreigners (Reiseausweis für Ausländer). It is only issued to foreigners who can prove it is not possible for them to obtain a passport from their home country. High costs or long processing times are not sufficient reasons for being issued with a grey passport. If you wish to try to get one, you need to document all your attempts to obtain a Venezuelan passport. Keep records of communications with the embassy, travel to the embassy, appointments, application forms etc.
Best,
Éanna