First, let us answer the second question. There is no clearly fixed age barrier; it directly depends on the country. In Germany, for example, the age of au-pair workers is 18–24 years, in France – 18–26, in Norway – 22–28.
Now about the States. The Au-pair program exists in the USA, but, alas, not for us. Uncle Sam gladly accepts Western fellow students, which cannot be said about Slavic brothers from the ever-developing countries of the once great and mighty. Even for such a popular program as Camp America (work in summer camps), only 20 places are allocated for all of dear Ukraine. The no less famous program Work & Travel (“Working, Traveling”) does not work in Ukraine at all. “They are ordered not to let us in” – and they don't.
What is in store for an applicant at the US embassy? As the blog of an extraordinary person wittily writes, with 99.9% accuracy they will receive a “blot” in their passport and show up in the database of refuseniks. And then try to prove that you are not a camel and that you never even thought of putting down roots in the freest land in the world.