This looks like someone who doesn't speak Irish or possibly Google translator.
"Do léigh" read, as in past tense of 'read'
"gaelach" means Irish or Gaelic as an adjective, not a noun.
You tell me.
The name Leigh is English.
It means "Irish pride".
rinceoir Gaelach ordamhsóir Gaelach.
Mo bhanphrionsa Gaelach = my Irish princess.
"gaelach" should be "na nGael" "Ádh mór na nGael a thabhairt duit" means "To give you good Irish luck"
Ceol Gaelach
Stobhach Gaelach
Gaeilge for the language; Gaelach as an adjective.
Croí Éireannach or Croí Gaelach
"beautiful woman"
"Conrós Gaelach" or "Conrós Éireannach"
Scottish Gaelic: Aingeal (if a name also Aingealag)Irish Gaelic: Aingeal
"Irish prince" could be 'prionsa Gaelach'/'prionsa Éireannach';