Learn Finnish: Kävimme katsomassa nukketeatteria kahdestaan. - The two of us went to see the puppet theatre.

This word uses the exclusive group size suffix -staan/-stään. When added to the weak stem of a number—in this case, the numeral kaksi (two) becoming kahde-—it means "exactly this number of people and no one else." Because the main verb kävimme (we went) is in the first person plural, context tells us kahdestaan means "just the two of us."

Can I use kahdestaan for "the two of them" or "the two of you", or is it only for "us"?

It works for all of those! While the suffix -staan/-stään historically contains a third-person possessive suffix, words like kahdestaan act as fixed adverbs in modern Finnish. The adverb itself does not change based on who the people are; you rely on the main verb's person ending (like the -mme in kävimme) to know if it refers to us, you, or them.

Why is katsomassa in the inessive (-ssa) case? Shouldn't it be a direction, like "went to see"?

In Finnish, the verb käydä (to visit / to go and return) requires the third infinitive (the -ma/-mä form) to be in the inessive case (-ssa/-ssä). Even though English translates this as "went to see," Finnish conceptually treats it as visiting while in the continuous state of watching. If the sentence used menimme (we went), it would take the illative direction form instead: menimme katsomaan.

Why is the object in the partitive case rather than the accusative?