1) That is not correct. GOD wont blindly attach his name to things that he doesnt want to be connected to. They may enter a life long pact with each other...but GOD is extremely choosey in who he attaches his Name to Nathan, and I dont think he would sanctify a Marriage that was not done before him, automatically, just because they are male and female.
The reason for this is because the concept of marriage is supposed to mirror the concept of the Church as Bride of Christ...AND of the relationships BETWEEN members of the Trinity. Mariage IS NOT a pact to spend ones life together Semper Fidelis, it is FAR more then that. The man and woman are joined, spiritually, as the Man was first bonded with his Mother as a Child.
Its about becoming two sides of the same person, and the same spirit, just as The GODhead is.
That is NOT something that can be possible in a secular or heathen marriage.
2) No, the reason every culture has the concept of marriage is due to Reproduction and continuation of their culture. It has nothing to do with being judged by any diety whatsoever. The best and most prolific way of reproduction, is a committed family of a man and a woman, who can then generate offspring, and nurture them.
Sorry, but even very basic animals have the concept of pairing off, creating their own home, mating, producing babies, and then rearing...I saw for the first time this afternoon, a Father Finch TEACH his Daughter to feed for herself, when she begged for food and her Mother wouldnt feed her. He picked a big bit of oat off the flight floor in his beak...took it up to the sill where she was perched and put it down infront of her...he then consumed half the oat and urged her to do the same...once she realized she could use her beak to peck and chop and carry...well...she was pecking EVERYTHING
3) Absolutely, which is why you can not assume that GOD will sanctify ANY union except those of believers. Whilst I reckon that he does sanctify some other Unions...I wouldnt dare claim it as factual...that would be like claiming that non Christians get to heaven. Its not good enough to be a human being who is judged on his life, any more then its good enough to be an athiest male and female being judged on their union. Belief in Christ, and ONLY that Saves, and ONLY GOD can Sanctify something permantly without a complex ritual that must be repeated gazillion times at a constant rate of perfection.
As the Jews tried that and failed (ergo the rituals of the Temple) I think you find that all Unions without GOD are simply a human promise, one to another. A marriage is way beyond that.