The Irish Gaelic version is Nóra, the Scottish Gaelic Nòra presumably.
In Scottish Gaelic: Uilleagan; Irish Gaelic is Liam
You need to specify Irish Gaelic or Scottish Gaelic: they are two separate languages.
There is no special spelling of the name in Irish or Scottish Gaelic: it would be the same as in English.
The name is not in Scottish Gaelic.
Names don't 'translate' unless they have a historical connection with the Gaelic cultures or are in the Bible.
The Irish Gaelic name Somhairle (Sorley) is equated with Samuel; also true for the Scottish Gaelic version Somhairle. It derives from the Norse Summarliethi/Somerled rather than Samuel.
The Irish form of the name is Nóra.
It's Scottish, but not Scottish Gaelic. Originally a Scots variant of Margaret.(Margaret is Mairead in Scottish Gaelic.)
Cheyenne is not a Scottish Gaelic word.
In Irish Mary is Máire. Is has no particular meaning in Irish, it's simply a phonetic translation. In Scottish Gaelic the name is Màiri.
Archie is a Scottish name.It has no direct Irish translation, but in (Scots) Gaelic it is usually written Eairdsidh, which is pronounced close to AIRchie.It's a familiar shortening of the name Archibald, which is the English equivalent of the Gaelic name Gilleasbaig (pronounced GILL-es-bick).
Anndra is the Scottish Gaelic equivalent of Andrew.