The Question and Answer section for Johnny Tremain is a great resource to ask questions, find answers, and discuss the novel.
Chapter One is set in Boston, Massachusetts at the Lapham home and silversmith shop.
That would be near the end of chapter 1. She gave him a cup to prove that he is related to Merchant Lyte.
This depends on what chapter you are referring to. I think it might be when his hand is mangled in the accident.