That's a lot of questions scrambled...
It is easier to get into a relationship with Sage being a DIK, it is easier to impress Bella being a CHICK, but those aren't conditions sine qua non. DIK players can impress Bella, CHICK players can be FwB with Sage, they just need to work harder.
At this point, DIK points only block getting into the 3way relationship with Maya and Josy; some side girls scenes require DIK affinity; and having a slice of Jill requires CHICK affinity. For now that's it. If affinity will funnel your options in following episodes is something only DPC knows.
Finally, NEUTRAL is, indeed, an option, but it is not a "best of both worlds" thing; it is a 3th option on its own, with perks and losses of its own (tho there is some overlapping).