Which prince is going to marry her?? Also is the prince already married to someone else???

In history, the 4th prince was kind and gentle compared to the 3rd prince.  The fifth prince was already married and loyal to the deceased king so he would always support the Queen.

 Kyubin:

That's wrong, especially starting by "in history". Sources are not clear, because contradictory, but historians consider now that they were four brothers, not five. Go Na Moo became king as the eldest after their father's death, and when he died, Queen Woo chose the third prince, future King Sansang, instead of Go Bal Gi. 

wiki

 Kyubin:

Definitely not a trustworthy source, especially for Korean history.

How come the drama uses the same information ie. there are five brothers instead of four.?

 Kyubin:

Because the screenwriter choose to follow this theory, for the sake of the dramatisation and fictional adaptation of these historical events, I guess. Historians consider they were only four brothers and King Gogukcheon was the eldest, so naturally succeeded his father.

Instead of using wikipedia as a source, anybody can easily find transcriptions of the "Samguk sagi" (an historical record of the Three Kingdoms of Korea: Goguryeo, Baekje, and Silla, written in the 12th century), which is the primary and only sources about characters and events of that time.

But as they changed many things, and invented even more, the drama is quite far from being close to the actual History. It's a very liberal and fictionalised adaptation of these events and historical characters,

People generally use wiki for everything and have no time to conduct research.  It's a dramatisation of a history for entertainment purposes so even if it is inaccurate, as long as the drama is good to watch, it doesn't matter.