Learn Finnish: Tilaisuudessa istumme vastakkain. - At the event, we sit opposite each other.

The suffix -kkain (or -kkäin) expresses a mutual arrangement between two or more things, often translating to 'each other' or 'together' in a physical sense. Here, it is attached to the root vasta- (against or counter) to create vastakkain, meaning 'opposite each other' or 'face to face'.

Could I use vastapäätä (opposite) instead of vastakkain in this sentence?

Yes, but you would need to add a pronoun to make the grammar work. Vastakkain is an adverb that means 'opposite each other' all on its own. Vastapäätä is a postposition, so you would have to say toisiamme vastapäätä (opposite each other) to get the same meaning. Using the -kkain suffix is much neater!

What is the base form of tilaisuudessa, and why does the stem change so much?

The base form is tilaisuus (event or occasion). In Finnish, nouns ending in -uus or -yys change that ending to -uude- or -yyde- before adding most case endings. That is why the base word becomes the stem tilaisuude- before we add the -ssa ending.

Does vastakkain always refer to a physical position, like sitting opposite someone?