Why isn't it "Tá háthas oraibh"? Don't you usually add a 'h' when vowels meet next to sequential words in sentences in Irish or is this an exception? I've also seen "Cá as tú?" and "Cá has tú?". Or is this just regional?
It isn't actually true that you usually add a 'h' when vowels meet - tá an is probably one of the most common word pairs in Irish, and the possessive adjective a only adds a h-prefix to words starting with a vowel when a means "her". There are some things in Irish that developed because certain clashing vowels can be awkward to say, but it definitely isn't a general rule.