"My sons are happy."
Translation:Mes fils sont heureux.
If a mother gives birth to two boys, she has two sons, or two children. It's the same. "Sons" is more accurate, setting the gender, but children is just as used in english, and fits perfectly in the sentence. I think it should be accepted.
While you might be close to yours sons, you may not be close to whoever you're speaking with. A polite conversation in a formal register would require "fils".
Yes, this is true, but both sentences are valid in the sense that we're trying to learn the whole language.