for those that seem to be lost:
Griffith was her "dad", the guy who was dying in chapter 1 who gave illie to kidou to take to her mother tania. Bug "boi" is probably tania, an experimental half human half bug (i am assuming this cause holy shit do the human parts look like illie). As for why they want her... that was just revealed. She can apparently cause the infection to manifest immediately in people above the age of 15 and then has complete control over those insects. In other words she is the queen of the Cagasters.
It's pretty straightforward honestly, pretty easy to follow.