Looks nice. First thing I noticed is that their homepage works without JS. However I am surprised that they didn't remove the account syncing stuff, which could also be achieved with an extension.
Ich kenne genug Leute die wegen der hohen Mieten aus Hamburg weggezogen sind. Das ist das einzig sinnvolle. Ich wurde niemals so viel Miete bezahlen dass ich davon arm werde.
This is correct. It could even be part of the application process. I would write them an email that the obvious fake one didn't work and you'll not put your SSN on that site for security concerns. Especially not in the application phase. If they reject you for that you have dodged a bullet.
Did anybody ever doubt this?