As for the "sodomite" thing:
The Hebrew phrasing has the same word, in male and female. No Israelite man shall be a kadesh, and no Israelite woman a k'desha. Simply put, "a male or female prostitute."
Presumably the female prostitutes in Biblical times were servicing male clients; were the male prostitutes hired by men or women? It's prostitution either way; but if you read it as the former, that would explain why your translation would call a person who services MSM a "sodomite."
My understanding of Maimonides is that his interpretation is about legal mechanics. When a couple is about to do act X, is it prohibited? Easy. If they're married to each other, no. If not, it's prostitution.
If you follow the interpretation that it was only prohibited Biblically if it was "a person open to anyone", then you can't really point to a single specific act or point in time that violates it.
I'll attempt to answer your other questions very briefly. Please consider asking them as separate questions.
- What's wrong with prostitution? Why God prohibits it?
Presumably sexuality is supposed to be something special (and holy) for the context of marriage. Note that Judaism says non-Jews shouldn't commit incest or adultery, but prostitution isn't prohibited for them.
- What does it mean by harlots and sodomites?
See above. Female and male prostitutes; your translation had colorful language.
- Now that we have paternity tests, do we still need marriage?
Yes. If nothing else, for the emotional bond. G-d says in Genesis, "it's not good that man be alone." A widower who already has children can decide whether he wants to marry a woman capable of childbearing or if he wants to be done being a father, but he is urged to marry someone.
- What does marriage mean?
Care to make that more specific?
- What about all non jews with different marital "deals". In jewish sense, they're not marrying right?
Wrong. See here.
- When contemporary civil marriage differ from biblical marriage significantly, which definition of marriage hold?
Between two non-Jews: if they call it a marriage ceremony it's a marriage ceremony, and we recognize it as such. (See link above.)
Between two Jews: if they choose to get married by a justice of the peace (or the like), rather than follow the Jewish marriage ritual, it's a matter of debate between 20th century rabbis whether Jewish law would recognize them as married. It's recommended they go do a Jewish ritual too (doesn't hurt anything); but regardless, if they split up, they should go through a Jewish divorce ritual.