Hello, Viracocha.

Pat-a-cake may be standardized, but I'm not sure about the other rhymes you mentioned. With regards to "A Sailor Went To Sea", the only part of that that I remember doing {as a handclap rhyme} is

A sailor went to sea sea sea
to see what he could sea sea sea
and all that he could sea sea sea
was the bottom of the deep blue sea sea sea.

-snip-

I bet there are other versions in the USA, but I can't think of them. You wrote that "A Sailor went to sea-sea-sea" [has](with many variations). Please share at least one or two of them.

And as for "A-B-C-Together"- I don't know that rhyme at all, unless you're referring to this jumnp rope rhyme:

All in together
Every kind of weather.
January, February, March, April, May {keep naming the months of the year until you miss. If you don't miss, then repeat the chant or "sing" another chant}.

-snip-

If your A-B-C together is different than that, please post the words! Thanks again, Viracocha!

Btw, it's great to find another Mudcatter interested in children's rhymes.