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1) Will I be able to marry her in Germany with my Swiss permit and Swiss travel document for refugees?
In order to get married in Germany as a foreigner you need a valid visa (“Visum zur Eheschließung”). You can apply for that at the German embassy in Switzerland as soon as the competent German registry office (see answer to question no. 2) confirmed that all required documents were handed in. The embassy will then talk back to German aliens department (“Ausländerbehörde”) and issue the visa after they gave their consent.
Source (German language): https://www.auswaertiges-amt.de/DE/Infoservice/FAQ/VisumFuerD/05-HeiratDeutschland.html?nn=350374
2) Are these documents sufficient for the marriage as per the German law?
In Germany the registry office (“Standesamt”) is competent for marriages. Your fiancé should go to the Standesamt in her city and ask them which documents you need to provide in order to get married. As stated above, you can proceed to apply for a visa after you handed in all the documents.
We had a similar question about the required documents in the community recently. Please check out the information provided here:
3+4) Will I be able to have a residence in Germany based on this marriage. And what kind of residency permit will I have in Germany then?
Marrying a German citizen grants you the right to live with your wife in Germany. You will receive a so-called residence permit (“Aufenthaltserlaubnis”) that is usually valid for 3 years - after that you get a settlement permit ("Niederlassungserlaubnis") if you fulfil certain criteria.
Sources (German language): https://www.rechtsanwalt.com/rechtsnews/rechtliche-regelungen-bei-der-ehe-zwischen-deutschen-und-auslaendern/
5) Will the marriage affect my status in Switzerland?
Unfortunately I’m not really familiar with Swiss asylum law, so I can only guess. I assume that you will lose your refugee status in Switzerland if it is replaced by a German “Aufenthaltserlaubnis”. But probably it’s best to ask the competent authorities in Switzerland (maybe the State Secretariat for Migration) about what’s going to happen if you two get married.