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 skags, who in turn have their weak point inside their mouths. This also means that the skags might be biologically related to The Destroyer.
Why is the city of Sanctuary named "Sanctuary" of all things, when it spends the entire game being terrorized by bandits and Crimson Lance? Because it sets up for the sequel, where New Haven, the main city in the first game, has been subjugated by Hyperion, and the heroes find sanctuary in -- you guessed it -- Sanctuary.
The fact that Commandante Steele doesn't use any Siren abilities when you finally fight her resurrected, Claptrapped self in the 4th DLC. Sirens have a mystical quality: there are only 6 of them in the universe at any given time, with a new one coming into existence whenever one of the 6 dies. It's likely Steele lost her Siren abilities when she was killed by the Destroyer, with her "place in the universe" immediately transferring to a new Siren. When you face her as Steele-Trap, her Siren tattoos are gone and have been replaced by Claptrap circuitry tattoos.
The loot dropped from the Destroyer is of lousy quality, generally no better than what would be dropped by a regular enemy. There's just a lot more of it (most of which is just ammo). This is in keeping with the Vault being full of nothing except "tentacles and disappointment".