Learn Finnish: Hän tulee sieltä. - He is coming from there.

It can mean either! Finnish does not have gendered pronouns. You use hän for both "he" and "she", and the exact meaning usually becomes clear from the context of the conversation.

The translation says "is coming", so why isn't there a word for "is" in the Finnish sentence?

Finnish does not have a separate "is doing" continuous tense like English does. The single verb tulee translates to both "comes" and "is coming". You should never add the Finnish word for "is" (on) next to another verb like this.

I thought the word for "there" was siellä. Why does this sentence use sieltä?

In Finnish, location words change based on movement. You use siellä when someone is staying in that place (stationary). Because the person here is moving away from the location, you must use sieltä, which specifically means "from there".

Can I drop the word hän since the verb tulee already tells us it's a third person?

No, you generally shouldn't drop it. While Finnish allows you to drop the pronouns for "I" and "you", you must usually keep third-person pronouns like hän ("he/she") so the listener knows who you are talking about.