Expect the remodeler to measure the floor, check the framing from below where possible, and talk through curb height, drain type, and glass. In an older Hull house, they may open a small section of floor first to see what's there before committing to a curbless design.
The building permit is filed with the Hull Building Department by mail, drop box, or in person, along with the contractor's HIC registration and Construction Supervisor license unless you file as the homeowner. The plumber's permit can be filed online, and because Hull's plumbing inspectors work part-time, the plumber should call to book the rough inspection before the walls close.
Before tile goes down, ask for a flood test of the shower base: the drain is plugged and the pan holds water for a set period to prove it's tight. It's a simple step that catches a leak while it's still easy to fix.