1) Jay would eat with his old group since he values their company and relationship he fostered with them over the past few years.
2) Yes. As a foreman, I would have approached Jay to welcome him to my team and make him comfortable in the new group and build new relationships as he meets the new members.
3) If I was in Jay's shoes, I would make an attempt to get to know the fellow mates. I would have joined the new group, introduced myself and take the opportunity to meet new people. I know that my old friends will remain and will always be there for me.