Learn Finnish: Hän menee pankkiin. - He is going to the bank.

Both! Finnish does not have separate words for "he" and "she". The word hän covers both, so you usually figure out which one is meant from the context of the story or conversation.

Why is the word for bank spelled pankkiin here instead of just pankki?

Because he is going into the bank. While English uses separate direction words like "to" or "into", Finnish adds a location ending directly to the destination word itself.

How does the "into" ending work in pankkiin?

For this specific destination ending (called the illative case), the general rule is to double the last vowel of the word and add n. Since pankki ends in an i, we stretch that vowel and add n, resulting in pankkiin.

Why is the verb menee instead of the basic dictionary form mennä?

Mennä means "to go". Because the subject doing the action is hän (he or she), the verb changes to match. In Finnish, verbs matching hän in the present tense almost always stretch their final vowel, which gives us menee.