“wedding guests.” The literal Greek is “sons of the bridechamber,” which was an idiom for the wedding guests; and in some contexts more specifically for the friends of the bridegroom who were at the wedding.
“groom.” In many English versions, the older term “bridegroom” is used, but it just means the groom.
“and then they will fast.” People fasted for different reasons, but often for a disaster or difficult situation, and to get God’s help with it, or to procure the favor of God. Jesus’ presence in and of itself brought “the acceptable year of the Lord” (Luke 4:19), and the grace and favor of his Father was upon him (Luke 2:40, 52; 4:19; John 1:14). This combined with the short duration of Jesus’ ministry on earth (likely just over a year; not the three years many people believe) in which he ate and drank with sinners, made physical fasting not the right choice. His disciples would fast after he left them.