Should I be able to say, "Den er barnets te," since I know the object is an "en" noun?
No. You would use 'den/det' if they replace a noun previously referred to. In this sentence it doesn't really do that. "Den er barnets te" would mean "Den teen er barnets te", which is redundant, and not common to say.
So basically the translation of "it" is det? Like we will use det for everything that contains it in English? For example: it is raining = det regner ute / it is red = det er rødt ?
Yes. The exception is if 'it' is a reference to a noun introduced earlier in the conversation. Then it can be either 'den' or 'det', depending on its gender.
"Det er en løve. Den er stor." = "[It/That] is a lion. It is big."
When would I use "barnas"?
barnas = children´s