His own public ship must be a good distance away. I suppose he didn't feel it proper to have it follow the luxury liner too nearby. Considering there were plenty of noble kids aboard, it might have been taken as intimidation if someone's private warship was always hanging around. The kingdom is, after all, quite divided in factions.
Of couse she has an inferiority complex. She's the only commoner in a school full of aristocracy. She has experienced bullying. Furthermore, in the original story she would already be close to the capture targets, that is, some of the most important dudes in the school, which majorly lessened the effects of bullying and isolation. She would have experienced some success as an adventurer, as well. So, she should have had a boost to her self-confidence. However, Marie seized all of that. The only positive experiences for Livia were Leon and Angie, but the bullies managed to turn even that against her. It makes perfect sense she wouldn't consider herself worthy of a nobleman, like Leon, in a strict feudal society.
It's actually quite funny that Leon keeps looking down on the capture target dudes all the time, but those guys actually let nothing stop them for the sake of player character in the game and Marie in the actual story. Whereas Leon tries his best to avoid any romantic development with Angie or Livia. So, Leon doesn't have the guts to fight against the norms of the society to get what he wants, whereas those good-for-nothing (in Leon's opinion) dudes do have the courage. Leon is actually the bigger loser here.