Learn Russian: Это мальчик? Нет, это не мальчик, это девочка. - Is this a boy? No, this is not a boy, this is a girl.

Нет means "No" and is used as a full answer to the question. Не means "not" and is placed right before the specific word you are negating (in this case, мальчик). You will often see them paired up to say "No, it is not": Нет, это не...

Why is the word "is" missing when we say это мальчик and это девочка?

In Russian, the present tense forms of the verb "to be" (am, is, are) are generally dropped. You just place the subject and the noun next to each other. So это мальчик literally translates to "this [is a] boy".

If мальчик (boy) is masculine and девочка (girl) is feminine, why do both use это?

When introducing or identifying something with "This is..." or "Is this...?", you always use the neutral word это. It acts as a set phrase and does not change to match the gender of the noun you are pointing at.

Does the negative word не change its spelling depending on the gender of the noun?

No, the negative particle не stays exactly the same no matter what comes after it. You simply place it directly in front of the word you want to negate, whether it is masculine, feminine, or neuter.