As it happens, The Water is Wide (the well-known one, that is, with the well-known tune) isn't an Irish song at all; it's English, and a collation of two or three separate Somerset variants (see thread here on the subject) published early in the 20th century by Cecil Sharp. In that form it was in copyright until fairly recently, though I doubt if anyone paid much attention. Sharp died in 1924, so I expect it's public domain now. I think Pete Seeger added a verse that he made up himself, mind you.

There is a lot of misunderstanding on the subject of traditional music and copyright, as some comments in this thread demonstrate. Although traditional songs in the general sense are public domain, specifics are often different: distinct variants may very well be in copyright as a consequence of having been published in print or on record. That won't prevent you from performing them, but there might be a modest royalty to pay if you were to issue recordings, for example.

All the songs you mention have been discussed here, some at length; have a look at those threads (you can find them via the onsite search engine - it's labelled "lyrics and knowledge search") and you'll get a better idea of how it all fits together. For specific answers, you'd really need to tell us exactly where you learned each one; and perhaps where the person you learned each one from learned them, and so on.