Learn Russian: Что-то происходит. Это какое-то важное событие? - Something is happening. Is this some important event?

The current lesson covers negative pronouns like ничто (nothing), which are used when something does not exist, and they require a 'not' (не) before the verb. Here, an action actually exists, so we use the indefinite pronoun что-то (something).

What does the -то part mean in какое-то?

Adding -то to a question word turns it into an indefinite word. While какое means 'which' or 'what kind', adding -то makes it какое-то ('some' or 'some kind of'). The speaker knows there is an event but doesn't know its exact nature.

Why do какое-то and важное have those specific endings?

They are matching the noun событие (event). Since событие ends in -ие, it is a neuter noun. Therefore, the modifiers take the neuter endings: какое and важное. Notice that the -то particle is attached after the normal neuter ending.

Why does the verb происходит take the 'he/she/it' form?

The subject of the first sentence is что-то (something). In Russian, the words что (what) and что-то (something) are always treated grammatically as singular and take the 'it' form of the verb.