I don't know what you mean by important facts, quotations, and events that take place in the play, but I'll give it a shot.
I'll begin with some of the facts. It is a fact that Henry Plantagenet and Elenore of Aquitaine were married and they had four sons. By the time play opens the eldest, Henry, is already dead. That leaves Richard, Geoffrey, and John. Henry is the king of England and Elenore is his queen.
When they met, Elenore was married to Louis, the king of France. The Pope annulled that marriage so that she could marry Henry. She was a very wealthy woman. She was also a woman willing to take a risk. She states in the play that when she went to the Holy Land, she imitated the Amazon warrior women by riding bare breasted. This is true.
It is also true that the two had a tempestuous relationship. It was no secret that Richard was her favorite and Henry kept her under lock and key because she had led a rebellion against him.
It is true that after Henry's death, Richard aka Richard the Lionhearted became king and was succeeded by his brother, John. This is the one and only John to have ever ruled England. He is the King John of the Magna Carta. Elenore, by the way, outlived her husband and saw both of her sons on the throne.
As for the events in the play they are probably fiction based upon facts. Did this Christmas meeting take place? Maybe, but the events depicted in the play happen only on stage. Was Richard betrothed to Alais? Yes, but they never married. Henry was known for having affairs so the affair between Alais and Henry in the play is quite possible.
Did Richard have a homosexual affair with Phillip? I don't know but it is possible and would explain why Richard never married...or maybe the reason he never married is he was too busy making a name for himself...or maybe, considering his role models, he just decided not to.
As for important quotations, that is really up to personal choice. Since I once played Elenore, my favorite quotes are from her. I don't know how important it is but I had a good time saying it. When Henry threatens to get rid of her as his wife and marry Alais she attacks him with his age and time and says, "How old is daddy then? What kind of spindly, ricket-ridden, milky, semi-witted, wizened, dim-eyed, gammy-handed, limpy line of things will you beget?" It was hard to learn but fun to say.
On a more serious note, one of my favorite Elenore lines is from this same scene (Act 2, scene1). "Life, if it's like anything at all, is like an avalanche. To blame the little ball of snow that starts it all, to say it is the cause, is just as true as it is meaningless."
Hope that helps you.