The impression I get is that he watched TOS as a kid when he was too young to understand many of its nuances but he's watched the TOS movies more recently and enjoyed them because of the increased action quotient (and in fairness I think this is important in a movie as opposed to a series). The absence of Chapel and Rand but inclusion of Chekov lends some support to this.
No, IIRC, JJ has explained in interviews that his introduction to ST was the gala world premiere of ST:TMP, as his Dad's +1. He knew that he didn't like TMP the way he'd loved "Star Wars" a few years before.
The choice of what characters to use in the movie was more likely to fall to Orci & Kurtzman.
The inclusion of Chekov at the beginning of the 5YM dates back to when Vonda McIntyre was writing "Enterprise: The First Adventure". Pocket Books specifically asked her to include Chekov
because his character had lots of fans who'd expect him to be included in a celebratory novel. (It was published for ST's 20th anniversary.) Remember that Orci & Kurtzman re-read this novel, plus a few others, when preparing their first ST script for JJ. Because of "Enterprise: The First Adventure", the film used the first names of Kirk's parents coined by McIntyre.