The phrase "given in marriage" goes back to the "primitive" notion that the wife-to-be, in particular, was given by her parents to the husband-to-be. Perhaps a better way of expressing the thought is she was entrusted to her husband-to-be. To this day, the idea that a man asks the father of his intended for "her hand in marriage" is not completely foreign to us, even in the West.
In Jesus' day, engagement and marriage were quite different from the way they are today, at least in the West. Back then, how the potential bride and groom felt about each other wasn't nearly as important as how their parents felt about the matchup. Moreover, a contract was formed between the two families well before the actual wedding day. It was called a betrothal. (Occasionally, even today, you might hear a variant of the word in the expression "pledge your troth.")
The betrothal, or engagement, was as legally binding as the actual marriage. First, each family would have to approve of the matchup. Then the bride price and the dowry** would be agreed upon, and they could take the form of money, livestock, land, precious stones, or really anything of value. If either the family of the groom-to-be or the family of the bride-to-be did not have the full bride price or dowry, respectively, they would be given a year or more to come up with the money (or the equivalent). In the meantime, the son and the daughter of the respective families would live separately but would be in what we today call an "exclusive" relationship. Another reason for at least a year's wait was to make sure the bride-to-be was not pregnant, which could be grounds for a divorce.
This exclusive relationship did not mean the couple was allowed to consummate the marriage (though it certainly happened from time to time), and most of the time they spent together until the wedding day would be in the company of a chaperone. No make-out sessions in the back of the car were allowed back then!
Consequently, if the bride-to-be became pregnant by someone other than her betrothed (as Mary, the mother of Jesus did, albeit by the Holy Spirit of God!), the husband-to-be could simply divorce her, in which case the bride-price would be returned to the father of the husband-to-be, and the contract between the two families would become null and void. Moreover, the bride-to-be was in danger of being stoned to death, at least within Judaism, since the woman was guilty of adultery. If that were to happen today in the West, there would be no divorce, though the husband-to-be might be entitled after the break-up to get the engagement ring back!
In conclusion, there is nothing "deeper" going on in the expression "given in marriage." As for its relation to monogamy, the man who had multiple wives would likely be the exception to the rule in Jesus' day, at least within Judaism, though outside Judaism, bigamy (or a wife plus mistresses "on the side") was perhaps more common, though the man would need to have considerable wealth in order to afford the bride price for multiple wives.
As for sexuality, there will be no need for it in heaven, for the simple reason that in heaven there will be no need for procreation, and God's command to "be fruitful and multiply" will no longer be in effect. The redeemed will then be like the angels who, though they always were identified as "men" do not marry (Mt 22:30; Mk 12:25; Lk 20:36). In heaven, the only wedding will be between the bride of Christ--the church universal--and Christ Himself, the Lamb of the Revelation of Jesus Christ (see Ephesians 5:25-32, and Revelation 19:7-10). That marriage will last forever and ever.
**From ISBE on "dowry": In all Hebrew marriages, the dowry held an important place. The dowry sealed the betrothal. It took several forms. The bridegroom presented gifts to the bride. There was the mohar, "dowry" as distinguished from matttan, "gifts to the members of the family" (compare Genesis 24:22,53; Genesis 34:12). The price paid to the father or brothers of the bride was probably a survival of the early custom of purchasing wives (Genesis 34:12; Exodus 22:17; 1 Samuel 18:25; compare Ruth 4:10; Hosea 3:2). There was frequently much negotiation and bargaining as to size of dowry (Genesis 34:12). The dowry would generally be according to the wealth and standing of the bride (compare 1 Samuel 18:23). It might consist of money, jewelry or other valuable effects; sometimes, of service rendered, as in the case of Jacob (Genesis 29:18); deeds of valor might be accepted in place of dowry (Joshua 15:16; 1 Samuel 18:25; Judges 1:12). Occasionally a bride received a dowry from her father; sometimes in the shape of land (Judges 1:15), and of cities (1 Kings 9:16). In later Jewish history a written marriage contract definitely arranged for the nature and size of the dowry.