Her parents are Empress Cadance and Queen Shutterbug. A fair bit of controversy surrounds her parents' relationship, being that Cadance and Shutterbug- an everyday newspaper reporter- met during a press conference. Some of the aristocrats disapprove of their relationship, not only because their 1000-year-old (or 10,000; I can't remember) selves are somewhat homophobic, but because Shutterbug doesn't come from royal background.
Yes, Shutterbug is just Chrysalis. But literally no-one knows about this except for Cadance herself. Not even Fern knows the truth, and certainly isn't aware of her own true form, either. Expect a fair bit of angst when she inevitably finds out.
I'll explain what happened to shining armour and stuff at a later date, rn I gotta go set the table for dinner.