In part, a team is defined by the things team members do together that other people do NOT do with them. The retrospective is the primary event that defines a team as separate from other people. If you split the team, the two new teams should be having separate retrospectives.
The standup is also a team defining ceremony, though not as rigid as the retrospective. I would suggest having separate stand ups for each team, with members from the other team invited to attend and only listen.
Shared or separate CI servers is more of a technical choice than one about team identity. Do what makes sense for the product development.
I don't know enough about your situation to tell if the iterations should be synchronized or not. Again, the needs of the product and its release cycles will strongly influence that decision.
Are you a full-time coach for the joint team? If so, maybe you can handle coaching both teams. If you are not a full-time coach, maybe you need to decide to make that transition. I'm just guessing here because the "right" answer is very dependent on the situation.
Don't allow an "us vs. them" culture to grow between the teams.
Policies about what? That is a huge question and odd to me. As a coach I do not strive to establish or reject policies.
Alan