Yes, in many cases, your children can automatically become U.S. citizens when you naturalize.

You can apply for a Certificate of Citizenship for your child by filing Form N-600 to have official proof.

If your child was born outside the U.S., you may also be able to apply for a U.S. passport directly.

If your child is over 18, they must apply for naturalization on their own they don’t get automatic citizenship.

Yes, but I guess it's only possible if they're under 18.