In the question “Are they married or not?” you said: “Some people who don’t have licenses are married in the eyes of the Lord and others who do are not.” Could you clarify what you mean at the end of the sentence?
Do you mean people who do not involve God in their ceremony (ie just going to a justice of the peace, or using some other religion, etc), or do you mean people who aren’t really committed to the marriage in their hearts (if so would that be if they weren’t even in the beginning or is it just if they are no longer, or maybe in cases of forced or arranged marriages, or marriages of convenience)?
I would think that even if people didn’t make the promise to God specifically, their vow to each other would still stand and He would consider them married.
This was my way of saying that some believers who are legally married do not meet the Biblical requirements for marriage as described in Ephesians 5:22-28 and other places. They are emotionally or physically unfaithful, unloving, and disrespectful to each other. Although at one time they may have been in love, these couples are divorced in their hearts and the only evidence they have that a marriage exists between them is a piece of paper from the government that means nothing in Heaven. They’re just going through the motions for the sake of outward appearances.
And what about the unbelievers among us? According to 1 Cor. 7:14 it takes at least one believing spouse to make the children of a marriage legitimate in the Lord’s eyes. From that you can conclude that God doesn’t recognize any marriage consisting of two unbelieving partners no matter where it’s performed or by whom, and considers their offspring to be illegitimate.