The alarm code is Jake's birthday, March 14th (0314). Alan enters an incorrect code.
When Alan is finished talking to Lenore, he does not turn off the phone. He just places the phone on the kitchen table.
It isn't really explained why, with the alarm going off for so long, the alarm company doesn't call the home or have the police roll by.
Jake explains that having a sushi bar in your bathroom would be cool, making the assumption that he likes sushi.
However, in "Squab, Squab, Squab, Squab, Squab" (s2e23), Evelyn tried to feed Jake sushi, but he hated it and spit it out.