Do you have Ausbildung duldung?As with that you qualify for help at the Sozial.
Also Altenpleger is not schulische as you are going to School and going Praxis.
Yes your kids qualify for residence 25a and you can read the law below and the requirements but you need to provide the passport
Granting of residence in the case of well integrated juveniles and young adults
(1) A juvenile or adolescent foreigner whose deportation has been suspended should be granted a temporary residence permit if
1. he has resided in the federal territory for four years without interruption either by virtue of holding a temporary residence or permanent settlement permit, by virtue of his deportation having been suspended or by holding permission to remain pending the asylum decision,
2. he has successfully attended a school in the federal territory for, as a rule, four years or has acquired a recognised vocational or school-leaving qualification,
3. the application for the temporary residence permit is filed before he reaches the age of 21,
4. it appears, on the basis of the his education and way of life to date, that he will be able to become integrated into the way of life in the Federal Republic of Germany and
5. there is no concrete evidence to suggest that the foreigner is not committed to the free democratic basic order of the Federal Republic of Germany