Why does joe want this?

Joe wants more than anything to die, because he wants to end this state of almost-death that he is in. He is unable to speak, see, hear, has no arms or legs, and so he is essentially unable to communicate or establish a connection with a human being ever again. He feels that he is as close to death as possible without being dead, because he is essentially dead but aware of it. However, he realizes that he is a one in a million that survives; most people that suffer the kind of injuries or even things less severe than him will die, and he feels as if instead of winning he is the one that has lost, because being in this state of conscious death is much worse than just being dead (although he does say for a passage that there is no abstract cause worth dying for). He didn't think he could ever win a one in a million draw, and everyone thought that he had won versus everyone else because he was the one that got to keep his life, but he sees it as a loss because he must suffer with this for eternity... or at least as long as his natural life lasts.

How injured is Joe?

Joe is seriously injured. He finds out progressively through the first part that he is deaf, then he is missing his arms, then his legs, then he is blind and has no face. He essentially has no ability to do anything, communicate, or express his thoughts in any way. However, he is not paralyzed, and his mind is completely intact, which is the worst torture of all. All he has is his mind and his consciousness and therefore that is how the entire book is narrated. It would be extremely frustrating... maddening in fact, to be able to be perfectly conscious and be unable to express anything whatsoever. One of his greatest desires is to die because he doesn't want to have to put up with this, and therefore he realizes that death for a cause isn't worth anything because he is the closest to death that is possible without actually being dead, so essentially he is aware of his "death" as opposed to someone who is actually dead who is presumably unaware of this, and from that standpoint he says that a person should always preserve their life.

Gender roles in once upon a mattress

As someone who spent a lot of time with this show, I had a lot of time to think about the gender roles. In a way it tries to defy them, but in defying them it still defines what they are. Dauntless and Winnifred are opposite roles in the sense that Dauntless is submissive and Winnifred is very strong and powerful. She even takes on a boy's name; "Fred" to show her manliness. Dauntless is ruled over by his mother. Queen Aggravain also has some distinct "gender personality". Women are often stereotyped as being overly talkative and annoying, and Aggravain certainly follows this. King Sextimus is, though very nice, afflicted with loose morals, chasing girls constantly. This also follows a stereotype; that women act like they don't want to be pursued when they really do, that it is ok to "trap" them (as the jester says "I will set a trap tomorrow". However, the musical mocks this stereotype more than following it, as it makes it extremely humorous. Lady Larkin's conversation with Winnifred struck me as interesting as well, because not only does Winnifred tell Larkin to apologize to Harry (Harry is the one that should apologize for blaming Larkin for mistaking the princess for a chambermaid), But she also tells Larkin not to act "too strong" because men like "weak women". This is very counter intuitive for Fred to say, as she is the ultimate "tomboy". I find it very interesting that Fred doesn't practice what she preaches, though its possible that she just knows Harry's personality and that he is extremely pompous and somewhat stuck up.

Finally, the song "Happily Ever After" covers the whole fairy tale stereotype, as there is one line that Fred sings in which she talks about how the "princess is always a bride" or something. She sings about how when she is married she will be happily ever after too, but she makes fun of this idea a little bit as well, even though it is obvious that though she is not the "typical" princess, she still wants the same thing that "typical" princess want.