How we cite our quotes: (Act.Scene.Line). Line numbers correspond to the Norton edition.
Quote #4
And therefore, since I cannot prove a lover,
To entertain these fair well-spoken days,
I am determined to prove a villain
And hate the idle pleasures of these days.
Plots have I laid, inductions dangerous,
By drunken prophecies, libels and dreams,
To set my brother Clarence and the king
In deadly hate the one against the other:
And if King Edward be as true and just
As I am subtle, false and treacherous,
This day should Clarence closely be mew'd up,
About a prophecy, which says that 'G'
Of Edward's heirs the murderer shall be.
Dive, thoughts, down to my soul: here
Clarence comes. (1.1.1)
Once again, Richard insists that since he's not a "lover," he's committed to reigniting the civil war that's torn his family apart. FYI – Shakespeare frequently associates wartime with a lack of sexual activity. For example, in Henry IV Part 1 Hotspur insists that women (and sex) will only interfere with his duty as a soldier, so he tries to remain celibate before and during battle.
Quote #5
A horse! A horse! My kingdom for a horse! (5.7.1)
When Richard's horse is killed during the Battle of Bosworth Field, he continues to fight on foot and cries out in frustration. There are a couple ways you could read this famous line. Richard could be saying, "Rats! My horse is dead and I'd give anything (even my kingdom) for another one!" Or he could mean, "Dang! I'm about to lose my entire kingdom all because of a dead horse!" Either way, Richard has lost all composure at this point and knows it's just a matter of time before he's taken down.
Quote #6
I think there be six Richmonds in the field;
Five have I slain to-day instead of him. (5.7.2)
Richmond has five guys dressed up like him in order to throw off the enemy during the battle. The trick works because Richard hasn't had any luck finding the real Richmond and has been killing Richmond lookalikes in a frenzy.
By the way, this was a pretty common military tactic. We see it in at least one other Shakespeare play: during the Battle at Shrewsbury in Henry IV Part 1, Sir Walter Blunt dresses like the king to help protect his monarch and gets stabbed in the guts for his trouble (5.3).