I admit I'm skipping ahead, so I didn't take the lesson that presumably leads to this one, but my answer, 'na páistí', is just as acceptable; 'an chlann' means 'the offspring', rather than 'the juvenile human beings', but I was given only 'the children' to go on.
"an chlann" means "the siblings", so the set of brothers and sisters. I guess "the offspring" is pretty much the same thing, but a little more of a technical biology term ish. I don't think I'd refer to my brother and sister as my "fellow offspring"!
No, definitely 'offspring'. Mo chlann means 'my family' in the sense of your sons and daughters and their sons and daughters. It doesn't include your brothers and sisters, though you and they are of the same clann in the sense of being descended from the same people.
No, "mo teaghlach" is "my family". So I have a "teaghlach", which includes my mother, and a "chlann", which is my brother and sister.
No, mo theaghlach means 'my family' in the sense of 'my household' or 'my nuclear family'. Your parents and siblings, traditionally also any servants and farmhands and such. A clann is composed of descendants of one person, but whoever is possessing the clann is its progenitor. Mo chlann 'my kids, my family, my descendants'.