"Banphrionsa". Prionsa is Irish for prince, and ban is woman, so it literally means "woman prince". It also feminizes the noun which is why "prionsa" picks up the letter h.
The Irish spelling is Ruairí; the Scottish spelling is Ruairidh.
You don't. Cheyenne is a non-Gaelic, proper name and, as such, has no Gaelic spelling.
Banphrionsa Ghaelach or Banphrionsa Éireannach in Irish;Scottish Gaelic: ?
Apparently the French spelling Céline is used by the Irish even when the last name is in a Gaelic spelling.
CIARÁN is the Irish Gaelic spelling; it is usually anglicized as Kieran.
The Irish spelling of 'amber' is 'ómra'. (Scottish) Gaelic:?
The Irish spelling of 'Sheila' is Síle. It is originally derived from Cecilia.
Spartach
I can't find any instance of an Irish Gaelic spelling for the name therefore it would be the same spelling as in English.
It could be Michelle or Miséil.A phonetic spelling is Miséil in Irish Gaelic but Michelle is also used.
'Iníon na hÉireann' in Irish;
The most common spelling is de Buitiléir or de Buitléir in Irish Gaelic.