I am unsure if there is a difference between paiste and clann. Can someone enlighten me please?
Clann is more "offspring" than "child". It can apply to multiple children of the same family, as well as extended family. Páiste just "child".
A páirc is usually only a field if it looks like a park - a field of grass can be called a páirc, but a field of potatoes or other crops is a gort, rather than a páirc.
See this discussion for references.
Note that there is a similar overlap between "park" and "field" in English when it comes to sports - we refer to Croke Park, for example, and many stadiums in England are called "Park" - St James' Park, Villa Park, Goodison Park, for example, but we refer to "the action on the field" ("pitch" is also used), and we say "a football field", not "a football park".
All in all, "park" is the most obvious correct translation for this exercise, even though "field" isn't entirely wrong, and you shouldn't assume a 100% equivalence between páirc and "field".