In looking for someone with the last name Praszker, I narrowed it down to someone born in 1930 +/- 5 years. Dawid was the only one who came up whose name started with the letter D.
There were a couple of people with matching addresses as Dawid. Some people (Dawid Majer (b. 1900) and Estera (b. 1889)) only lived at the Rauchgasse address, which leads me to believe that they were probably an uncle and aunt of Dawid. The other adult figures, Hersz (b. 1908) and Ruda (b. 1910), lived at both the Rauchgasse and Pilsud addresses, which makes me think that they were probably Dawid's parents, but we can't be sure.
The other members of the famiy were two siblings (or cousins), Abram (b. 1929) and Jakob (b. 1931).
As far as fates, the potential uncle Dawid Majer has a change of address date (along with a message 'Na Rob') of July 1, 1942. The potential aunt Estera was deported (most likely to Chelmno) on September 11, 1942. No deportation information was listed for either parent Hersz or Ruda. Abram has a change of address date (to Buchbind 3) on December 6, 1942. Jakob has a note that said UMELD, and I'm not sure as that meant.
Dawid died of currently unknown causes on August 30, 1942.