Narses has given you the correct answers, or pointed you where you can find them.
Baptism CAN be performed by an lay person with correct intent, matter and form. Normally that would only be done if there is some good reason to do so--otherwise, it would be done in church by a priest with sponsors.
Also, the Catholic Church keeps records of baptism, so it should be reported to the baptized person's parish church (possibly chosen after baptism) and entered into the records. And the priest might decide to do a conditional baptism in addition, to be sure that everything was valid.
Marriage is the other sacrament that can be performed by lay persons. In fact, the bride and groom administer the sacrament to each other with the ring and the words, and the priest is said to preside over the sacrament. Non-Catholics also can validly marry, but not sacramentally. Catholics normally should marry in church at Mass, presided over by a priest, and properly witnessed, but as with baptism can marry one another privately if there is a sufficient reason or emergency, and then have it confirmed or preferably performed again in church with a priest and witnesses. At least, that is my understanding.
Yep. My Dad is 86. I just found his Baptism cert from 86 years ago, and promptly tacked it to his wall. Same with the Confirmation cert.
Really fascinating. Thanks.
As regards marriage, are non-Catholic marriages those not sacramentally married, should those also be remarried with a priest and witnesses?
Thanks.