Germany issues three different kinds of fictional certificates and the answer to your questions depends on which type you have. Based on your circumstances (waiting for the decision upon your first appplication for a residence permit), you will have been issued a fictional certificate based on § 81 Abs. 3 Satz 1 AufenthG. You will find a corresponding notice on page 3 of your certificate.
No. A fictional certificate based on § 81 Abs. 3 Satz 1 AufenthG does only grant you the right to stay in Germany until your application for a residence permit has been decided upon. You are right that there are usually no border checks when travelling within the Schengen area, but that does not necessarily mean that everyone is entitled to cross at an unstaffed, seemingly open border crossing. Both because of the covid situation and also still because of the 'refugee crisis' in 2015, immigration checks are much more common than they used to be on intra-schengen borders. Since you are planning to go to Hungary, all land border crossings from Hungary towards Austria are for example now permanently staffed. When crossing that border by car, I have some times been waved through, but also been stopped for a document check.
At least not because of the fictional certificate. It does not give you a right to reenter Germany if you decide to leave. If you are allowed to reenter, will in your situation depend on a fine count of the days you have already stayed in the Schengen area. There is no 'reset' of the 180 days as you seem to believe, but you are only allowed to stay 90 days within any floating period of 180 days. If you stayed 14 days in September, reentered on October 1st and for example leaves Germany on December 15th for your Christmas holidays, that will make up 90 days. You will then not be allowed to reenter Germany (or any other Schengen country) until 180 days after your entry in September. Depending on when you exactly entered in September, that will not be until late February or some time in March.
Addition: I am not going to participate in another fruitless discussion with Mark Johnson, I just wanted to explain why his answer is wrong. You can in the 'General Administrative Provisions for the Residence Act' (only available in German), in section 81.3.6. find the relevant clarifications regarding your fictional certificate. Here, it is clearly explained, that your fictional certificate does not count as a replacement for any of the credentials you are, according to the Residence Act section 4, required to be in posession of when entering Germany, among them are national visa, temporary and permanent residence permits. And to quote the relevant conclusion:
Anders als die Fiktionsbescheinigung, die nach Absatz 4 erteilt wird,
erm?glicht die Fiktionsbescheinigung nach Absatz 3 daher keine
Einreise in das Bundesgebiet.
Or my translation:
Unlike fictional certificates, which are issued based on section 4,
the fictional certificates issued based on section 3 (my remark: § 81 Abs. 3 Satz 1) do therefore not
allow you to enter the federal territory.
For the counting of 90 days to be interrupted while you are within the Schengen area, you need to be in posession of a national visa or a residence permit and be present in the country, which issued these documents. Since, based on the provisions I referred to, Germany does not consider your fictional certificate as a replacement for a national visa or a residence permit, being in Germany with a fictional certificate based on § 81 Abs. 3 Satz 1 does not interrupt the 90 days clock.
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