Learn Dutch: Zij verstopt de geheime doos.

Look at the verb! Verstopt ends in -t, which is the regular present tense ending for "she" (third-person singular). If zij meant "they", the verb would take the plural form: Zij verstoppen de geheime doos.

Can I use Ze instead of Zij here?

Yes, you can. Zij is the stressed form, used when you want to emphasize that she is the one hiding the box, not someone else. Ze is the unstressed form and is very common in everyday speech if there is no special emphasis.

Why is it geheime instead of just geheim?

In Dutch, adjectives get an -e at the end when they come right before a noun, like in de geheime doos. You only leave this -e off when the noun is a het word and it comes after een (a/an) or has no article.

How would this sentence change if she hid "something secret" using the indefinite pronoun iets?

You would say Zij verstopt iets geheims. When an indefinite pronoun like iets (something) or niets (nothing) is followed by an adjective, the adjective gets an -s at the end instead of an -e.