'tá ... ó' is the idiom in Irish for 'to want'. You've seen lots of these in Irish, such as 'tá ... ag' being used for 'to have', but English has these too, lots of them.
Take the phrase 'I get off the horse': what exactly are you 'getting' in that? Is it help? No. Rather 'to get off' is the native idiom used in English for 'to dismount'.
Similarly, 'tá saoránach uait' literally means '(a) citizen is from-you', but actually translates as 'you want a citizen'.
Almost. It just means 'want', not 'want to have'. As with the verb 'want' in English, the manner in which you want to interact with the thing is implicit.
For instance, if I were to say 'tá pluiméir uaim', that means 'I want a plumber', with the implication that you want them to fix your plumbing or talk to them about it. However, if I were to say 'tá uachtar reoite uait', which mean 'I want ice cream', then the implication is that I want it so that I can eat it, or maybe give it to somebody else for them to eat.
Of course, all that is implication. Without further context, it could as easily mean that you want a plumber because you're a cannibal, or that you want an ice cream to fix your plumbing.
It definitely doesn't mean 'want to be' though.