Cape and Nantucket native Meghan Trainor was home Thursday to surprise students at her alma mater, Nauset Regional High School. Her appearance was private, but we’ve been told that the “All About That Bass’’ singer and Grammy nominee spoke to students, gave a quick performance of her big hit and her second single, “Lips Are Movin,’’ and made time for some photos, which were quick to turn up on social media. Trainor, who graduated Nauset in 2012, announced Sunday that the first song on her new album will be called “No.’’ Students tell us her appearance was taped for television.