This is about the movie, not the book. The movie doesn't get a free pass for not filling in its plot holes just because they're explained away somewhere else.
7. How does Inigo still have his father's sword?
Inigo Monotoya is a man consumed with revenge. We get the feeling that he tells his tale of childhood trauma to anyone who will listen, to the point where pooping in a the stall next to him is a dicey proposition. So it's not a surprise that this story is among the first topics of conversation Inigo has with The Man in Black. The first chance he gets, Inigo tosses his sword over to his opponent so that he might better admire its crafstmanship, mostly because it helps his story have more impact.
We learn that Inigo's father was commissioned to produce this very sword by a person only known to Inigo as The Six-Fingered Man. The finished product was a masterwork which the Man in Black admits is peerless, but the buyer was not impressed. In a dick move straight out of the Craigslist for Assholes handbook, the Six-Fingered Man offered ten percent of the original, agreed-upon sum. When Inigo's father refused, the Six-Fingered Man murdered him in cold blood and gave the pre-teen Inigo a few scars for his trouble.
So uh, why does the Six-Fingered Man leave the best sword in the world with a 10 year-old kid?
Inigo talks about the sword like he's had it all of his life, and it's the weapon he uses when he battles the Man in Black. Are we really to believe that the Six-Fingered Man -- the same ruthless asshole who came up with a life-draining machine -- wouldn't want to take two seconds to yoink the super-special sword made just for him? Six-fingered swords have gotta be hard to come by, and you just know that prick would love to carry that blade as a morbid trophy of his misdeeds.
Seeing the Six-Fingered Man get impaled by the sword of a man he killed is satisfying, to be sure, but that justice would be all the sweeter if Inigo spent the movie searching for that sword. In taking his father's work back and using it against the perpetrator of that foul crime, Inigo would also be taking back his life. I guess "My Name Is Inigo Montoya, Please Give Me Back My Father's Sword, Prepare to Die" doesn't have the same ring to it.
6. Why did Westley wait so long to tell Buttercup he was alive?
As everyone knew the moment he stepped on screen, the Man in Black turns out to be Westley, the long-lost love of Princess Buttercup and bane of god-fearing Wesleys everywhere. The prologue explains that the two fell for one another on a humble farm, and Westley eventually left to seek his fortune to build a better life for the two of them. Of course, for the sake of the narrative, the two were ripped apart when Westley's ship was set upon by the infamous Dread Pirate Roberts. This is the same pirate that is known for never taking captives (preferring to kill them), so Buttercup rightfully assumed that her Westley was dead.
But since the story doesn't end there, we learn that Roberts secretly took on Westley as a ward, eventually training him to be the new Dread Pirate Roberts. Meanwhile, Buttercup has been languishing in grief for half a decade.
For five years, Buttercup was absolutely wrecked, her soul hollowed by the thought of never seeing her true love again. And Westley just let her suffer. At no point during those five years does Wes bother to send a letter or any sort of signal. If he was worried about being found out by the rest of the pirates, all he'd have to do is code the letter in such a way that gets his message across. Something like "I am still coming for you. I might be a while, but please wait for me. If you can, put some of the leftover stir fry in some tupperware in the fridge, but if you can't no big deal" would be more than adequate.
But okay, let's say that he was too afraid of the Dread Pirate Roberts to make a move. After all, the last thing Westley heard before bed every night was nothing short of a threat on his life.
So at some point after three years, Westley becomes the Dread Pirate Roberts. Which means that he had around 24 months to contact Buttercup, but neglected to do so, despite being the captain of the most feared ship on the high seas. Wes had all the time in the world to swoop in and whisk away his beloved, but Wes inexplicably waited until Buttercup's kidnapping to finally show up. And THEN he has the gall to get angry with Buttercup for marrying another, when he basically was going out of his way to hide the fact that he was alive.
Man, Westley's kind of a dick, isn't he? What could Buttercup possibly see in hi--
Oh, right. It's kind of hard to stay mad at Tiger Beat's Farmboy of the Month. If you could, you'd wait five years for a ride on that dreamboat, too.