I notice that they didn’t explicitly mention the ESC by name once in the episode. did they have difficulty getting the rights to that?

Probably - it makes me think of how UNIT no longer refers to the United Nations.

how Kid got into the station in the first place.

I assume he had a ticket. Hellions may be marginalized, but it seemed like they are treated poorly, rather than legally segregated from society.

they’re making bigeneration a general thing

There's no such thing!