The whole philosophy of time really irritated the heck out of me. So... you can't change anything that happens, yet you still engage in conversations and can talk to people - if it was impossible for you to use your 4-dimensional senses to influence anything, you would be unable to communicate the fact that you had them. You can choose what time you're experiencing, but don't have any control over it? The whole thing strikes me more as "some aliens have a really stupid view of how memory works" than anything profound.
Still, judging how Kurt Vonnegut wrote the book, you may not be too far off.
Actually the Tralfamadorians only exist inside Billy's head and they only exist to convince Billy why he can't change anything. The reason Billy never makes an attempt to change anything is because he thinks it is all hopeless and can never be changed and so he basically created the Tralfamadorians to convince himself of this.
From what I can tell, Kurt Vonnegut really, really hates the notion of free will, and he adopts the notion of a block universe wholeheartedly. How he could possibly reconcile this with time travel of the form he describes is utterly beyond me. See the execrable book Timequake for another example of how this version of time travel makes no sense whatsoever.
Slaugtherhouse-five is an indictment of the type of behavior the Tralfamadorians and Billy Pilgrim exhibit. Re-read the introduction, or the other wiki's article on it; it's all satire, if Kurt Vonnegut really hated the idea of free will and thought everything was predetermined, do you really think he would have had the Tralfamadorians know that they'll blow up the universe with their experimental saucer fuel? The message is not that there isn't anything that you can do to change the future, it's that fatalist thinking leads to catastrophes and terrible, awful things like the fire-bombing of Dresden and all of existence ending because of a (very, very,) preventable accident.
Three more parts of the story that indicate that Vonnegut is anti-fatalism: first, the scene of Billy's death. As with the Tralfamadorians and their universe-destroying spaceship, Billy is fully aware of what's about to happen to him. He knows when his death is coming, and has a big ceremony to mark it. He also knows that putting this ceremony on in the first place will attract Paul Lazarro and his hitman to come and murder himself, He then ignores the protests of the crowd around him to seek shelter, and demands that his police escort leave him be. Then he gets shot. Billy does EVERY SINGLE POSSIBLE THING he can do to get himself killed, If he hadn't put on the ceremony, or kept his escort, he would still be alive. It's his fault and no amount of fate can remove the blame from him. Second, Vonnegut states his intention to write an anti-war novel, and a friend suggests writing an anti-glacier book instead. Vonnegut states "what he meant, of course, was that there would always be wars, that they were just as easy to stop as glaciers. I believe that, too." Yet despite agreeing with his friend that wars won't go away so easily, or at all, he still writes his anti-war book. If he was such a fatalist, why would he bother? Third, this line from the final chapter, narrated by Vonnegut: "If what Billy Pilgrim learned from the Tralfamadorians is true, that we will all live forever no matter how dead we sometimes seem to be, I am not overjoyed." Vonnegut states outright that he disagrees with the Tralfamadorian philosophy. (Incidentally, this is why the book's Arc Words seem so bland and uncomforting—they really are bland and uncomforting.)
Addressing the original philosophy of time confusion: Billy does not choose when he jumps in time, it happens completely at random. Imagine being able to remember something in your past so perfectly that you might as well have lived through it again. Then imagine being able to see the future in the same way. That's what it means to be Unstuck In Time. Also, if the story is looked at from a normal, stuck-in-time perspective, Billy never mentions his knowledge of Tralfamadore or being unstuck in time until he returns from his abduction. To anyone that isn't experiencing what he is, Billy is just a confused soldier, then an optometrist, and then suffers a severe injury in an airplane accident and starts babbling about seeing the future.
Fridge Logic: How did Billy and Montana Wildhack have a baby on Tralfamador if there are 7 human sexes needed for reproduction?
Generally, scholarly discussion holds that it's all a fantasy in Billy's head after the plane crash, both because of this, because of Vonnegut's use of irony, and the sheer impossibility of him being killed on Earth by Paul Lazzaro if he lives out all of his life on Tralfamadore.
The same way everyone else has a baby. Seven human sexes do not have to be present at that particular moment in time...it actually says that most of the sexes are in the fourth dimension, with homosexual men (but not homosexual women), babies who die shortly after birth, and women over 65 being listed as essential to the process. Presumably, all of the sexes like this had already played their parts (however those parts are played).
This troper has seen two schools of thought on this passage — one being definitive proof that the Tralfamadorian bits are untrue, and that Billy just isn't smart enough to see that his own world contradicts itself; or alternately that there's more to the whole scene than first seems, with hints of Billy's homosexuality, the possibility of a dead baby beforehand, or even just a larger zoo with more people in it. i think the first interpretation is more commonly accepted, but it is Vonnegut, so he might've meant both.
It's also possible that, since it happens in the fourth dimension, Billy and Montana are the only components of the equation that need to be close to each other in the third dimension. Everyone else could potentially be millions of light-years away in the third dimension, but touching in the fourth.