Marriage is not a "delicate entity," and there are not marauding government teams going door to door to ensure that marriages are valid. The government does not actively investigate marriages to ensure that they are valid.
Further, there is literally no difference in research required for a ICE agent looking into a heterosexual marriage and one looking into a gay marriage.
Literally none.
Marriage is by definition a sexual contract, so it is expected in healthy circumstances that the man would want to have intercourse with the woman. If your lesbian friend married someone, then he would have the legal right to have intercourse with her. It would be very difficult for her to prove that it was non-consensual rape. If he paid her for the green card marriage, then she would go to jail.
No, it is not. You are advocating in favor of marital rape, which I would like to point out is a crime in just about every civilized, Christian country. A wife is under NO obligation to have sex with her husband if she does not wish to, and if a husband forces himself on her anyway he can — and should — go to prison.
Your logic is vile and perverse.
The end.