Learn Russian: Какой карандаш твой?

Because карандаш (pencil) is a masculine noun. The question word какой (meaning which or what kind of) must match the gender of the noun it describes. If we were asking about a feminine noun, we would use какая.

Why is there no word for is in this sentence?

In Russian, the present tense verbs for am, is, and are are almost always left out. The sentence literally translates to Which pencil yours?, but it is perfectly understood as a complete sentence.

Does твой also change its ending based on the noun?

Yes! Just like какой, the possessive word твой (yours) must match the gender of the noun it refers to. Since карандаш is masculine, we use the masculine form твой. If it were a feminine noun, it would be твоя.

Can какой mean what kind of as well as which?

Exactly. Depending on the context, какой can mean which (choosing a specific pencil from a group) or what kind of (asking about its color, size, or type). Because we are asking about ownership here, which makes the most sense.