Hi @Andrey_Malk
Firstly, congratulations on getting the Ausbildung!
Answer 1:
If you withdraw your asylum case, you have the possibility of the residence permit 16g or the status of Ausbildungsduldung. The regulations are complicated but to put it simply, if a person doing an Ausbildung has enough money to support themselves and also a passport, then they will receive the full permit 16g. If they do not, then they receive an Ausbildungsduldung.
It is important for you to know that if the Ausbildung does not pay enough for you to live on, you can get the benefit BAB (Berufsausbildungsbeihilfe) from the Agentur für Arbeit. If this is still not enough, you can also get some additional benefits from the Jobcenter (Bürgergeld) in order to show you have enough money to live on.
You can first apply for 16g or the Ausbildungsduldung seven months before the Ausbildung begins. The permit 16g or Ausbildungsduldung can first be issued six months before the start of an Ausbildung.
Answer 2:
The time you spent until now in Germany with the paper Aufenthaltsgestattung will not be counted as legal residency towards the time needed to become a German citizen. Only once you have been issued with a residence permit does the time count. However, under the new law on citizenship, 5 years will only be the standard amount of time required. For people who can show they are well-integrated (i.e. having a German qualification, level C1 of German) this will be possible after three years.
With certain types of residence permits, it is not possible to change from them to becoming a citizen. While the new permit 16g is not listed among them, I presume it will also be included as similar permits like 16a and 16b are. This means you would first have to change to a permit as a skilled worker or acquire permanent residency before being able to apply for citizenship.
This rule is covered in paragraph 10, section 1, part 2 of the law on citizenship:
https://***.gesetze-im-internet.de/stag/BJNR005830913.html
Best,
Éanna