Can they baptize, without the godparents or parents having made the first communion? Our parents never took us to classes.

God parents are not needed. Talk to your Pastor. Don't worry.

The godparents must have all the Sacraments and if they are married they must be married by the Church. But you as the only parents have to be baptized. If you would like to complete the sacraments we have RCIA / RCIA classes in Spanish and English.

I do not think so, but I'm not sure.