Learn Russian: Чей это карандаш?

Чей means "whose" for masculine nouns. It has to match the gender of the object you are asking about. Since карандаш (pencil) ends in a consonant (ш), it is a masculine noun, so we must use the masculine question word чей.

If карандаш is masculine, why does the sentence use the neuter word это instead of этот?

In this sentence, это acts as a generic pointer meaning "this is" or "is this". When used as this standalone pointer, это is a fixed word that does not change to match the noun's gender. You would only use the masculine этот if you were attaching it directly to the noun, like in the phrase этот карандаш (this pencil).

There is no verb for "is" in this sentence. Is that correct?

Yes! In the present tense, Russian almost always drops the verb "to be" (am, is, are). So, Чей это карандаш? literally translates to "Whose this pencil?", and the "is" is simply understood from the context.

Could I change the word order and ask Это чей карандаш?

Yes, you can. Russian word order is very flexible. However, Чей это карандаш? is the most standard and natural way to ask. Putting the question word (чей) right at the beginning clearly signals right away what information you are looking for.