Learn Finnish: Jokin tapahtuu. - Something is happening.

In standard Finnish, jokin means "something" (used for things) and joku means "someone" (used for people). Since an event is a thing, we use jokin. However, in casual spoken Finnish, you will often hear people use joku for both things and people.

Why are there no accusative pronouns (like minut or sinut) in this sentence if that is what we are currently learning?

The verb tapahtua (to happen) is an intransitive verb. This means the action just happens on its own and isn't done to anyone or anything. Because there is no target or "object" receiving the action, we don't need an accusative pronoun here.

Does tapahtuu mean "happens" or "is happening"?

It means both! Finnish does not have a separate continuous tense (like "is happening" in English). You use the standard present tense tapahtuu, and the exact meaning comes from the context of the conversation.

What is the dictionary form of tapahtuu, and how is it formed?

The dictionary form is tapahtua (to happen). It is a Type 1 verb. To get the third-person singular ("it" or "something") form, you take the stem tapahtu- and double the last vowel, resulting in tapahtuu.