Why can't Lilith jump while Phasewalking? For the same reason that she takes no damage and can't open doors or operate machinery while Phasewalking. Energy, whether kinetic, themal, or electromagnetic, cannot affect her body while she's Phasewalking, and vice-versa. She cannot exhibit kinetic force on any object in our dimension, and thus she can't push against the ground to propel herself upward. A brilliant and subtle case of Magic A Is Magic A.
Look closely at the Fast Travel station in New Haven. If you pay attention to where it is located, it is outside the barriers that inhibit vehicle access to the interior of the city. Why would someone want to put that there? So in case bandits hijack the Fast Travel station, they'll pop in outside the barriers and city's defenders will have cover to gun them down.
When you open the Vault and have to fight The Destroyer, Angel only mentions that you know where to hit it to kill it, which left many players confused since there was no previous hint of its existence. However any player who payed attention to Pandora's wild life should recognize that the Destroyer has the same split jaw and 4 eyes anatomy as the skaggs, who in turn have their weak point inside their mouths. This also means that the skaggs might be biologically related to The Destroyer.