Thank you very much, you all! I have received a lot of great answers here and by mail.
First, I have to say that I am a beginner in Jewish Genealogy (in other a complete noob). So thank you for bearing with me.
Second, I will now give you all information, I have about the family in question, as I see how difficult this research has become. Ask me if you need more information.
The following facts are confirmed by primary sources (in German) written either in so-called synagogue books (Jewish) or church books (Christian).
The starting point is a woman, who seem to have converted to Christianity. Her name is Caroline Pauline Reichenheim, she was born around 1805 in Dessau (as the 3. daughter).
Her father was mentioned as already deceased one her marriage entry in 1834 (Christian source) and named with his Yiddish name as Löser Reichenheim.
In his death entry in the synagogue book (Jewish source) from 1826, he was called Lazarus Abraham Reichenheim. His age was given, so he must have been born either 1760 or 1761, probably in Dessau. It was called a "Schutzjude" in that entry.
From another source (Christian), I know for certain that Caroline P. Reichenheim had 2 children before she married, which later had the same surname of her Christian husband. In the synagogue book I found that the only 10 days after the known birth of her first child, a child was mentioned with the name of her father with his Yiddish name as Loser Reichenheim and a woman called "Pesche", which I believe stands for "Elisabeth".
Interestedly, there is another child mentioned, Abraham Reichenheim, with both her parents. This child was not known to me before. The third (actually second) child I know she had before marrying his not written in the synagogue book.
It seems that this family had 5 daughter, 4 of whom are know by name. One seems to have converted to Catholicism (confirmed indirectly in German newspapers) and I have found a baptism record for another daughter, where her mother is indicated (Christian source).
A mother was indicated as: "Henriette, geb. Itzig". "Geb." is the abbreviation for "geboren" or neé in Englisch, so it seems to indicate a surname. However, it was only found in a baptism entry of a church book (Christian source). On this baptism record, the father was named as Lazarus Hirsch Reichenheim.
Despite these name variants, I am quite certain that they are all from the same family, as there seems to be extremely few Reichenheim among the Jewish communities in Anhalt (state back then). The only, rather successfully Reichenheim, were those originating from Bernburg (a town nearby) which moved in the 1830s to Berlin to make a fortune until the rise of the Nazis.
The issue that I have is that the synagogue book at hand starts at 1811. I know that there is another one from 1786 to 1810, but I have no access to it (at the moment).
On FamilySearch, I can only get my hands on the above posted "burial records", where I hoped to get more information, see above.
Now, that you were able to conclusively determine the death or burial date of a Hirsch Reichenheim. I guess that this might be the father of Lazarus Abraham Hirsch Reichenheim.
Would the next step would be for me to go through the register to look for a woman called "geb. Reichenheim" = "neé Reichenheim"?
Another question is, is it true that in Jewish culture a married couple is buried in their own graves with separated grave stones? if so, with which name is the wife buried?