
Question: Is there any reason why Luke believes what Darth Vader says when he tells him that he is his father?
Answer: The vision Luke sees in the cave on Dagobah is a clue to this. Luke is realizing he has a lot more in common with Darth Vader than the idealized father he'd always imagined. When Vader tells him he's his father, Luke doesn't want to believe it, but he simply can't deny that it feels much more true that his father would be someone passionate and reckless like himself rather than someone who exemplifies a noble Jedi, which feels like an obvious myth in hindsight.

Question: How was Obi-Wan going to become more powerful after he was dead?
Answer: It is heavily implied that one who becomes a Force-Ghost achieves an untold level of power upon entering the state. Given that they have become a pure entity of the Force, it seems to back up the statement. Obi-Wan also becomes free to assist Luke in any case.
In addition to this answer, I think Obi-wan also became powerful because he "let go." He did not feel a need to defeat Vader on this occasion - he was willing to surrender the fight and "move on" to a new state. Something that Vader might not currently understand.

Question: Does Vader sleep in his suit?
Answer: Darth Vader has a special chamber in which parts of the suit can be removed for comfort. When he is not in the chamber he must wear it at all times in order to survive.
Answer: Darth Vader does have his own personal chamber made to assist him with the equipment /suit he wears as well as, I'm sure, for resting/meditation purposes. Also keep in mind that Jedi/Sith, especially those trained to use the force (particularly those having mastered it), don't need the same sleep requirements regular folks need. They can "sleep" sitting straight up, on top of much harder elements and they can even "draw" energy from the force to help them stay awake. The expanded universe, via the books, gives more examples of Jedi/Sith sleeping or measures they take.

Question: After Anakin becomes Darth Vader, he seems ruthless, actually evil. "From my point of view, the Jedi are evil!" Is just one quote. That being the case, this movie makes it seem like Anakin knows that he's evil and wishes he wasn't. Basically, my question is, why didn't Anakin turn on Palpatine sooner? Or simply leave the Sith?
Answer: Darth: "Obi-Wan once thought as you do. You don't know the power of the dark side. I must obey my master." It's implied that the dark side is intoxicating, once you totally give in to the dark side it has a hold on you, and appeals to morality and rationalization are useless against your lust for its power. (On a symbolic level, the dark side is a metaphor for vice. Darth Vader is an addict and abusive parent. It's actually funny how many scenes still make sense if you replace "the dark side" with "the bottle" or similar).
If we bring the prequels into it, it's one of the criticisms of those films that they only make the question of how much Anakin is a "true believer" more confusing. But it stands to reason that at first Anakin may feel vindicated in his resentment toward the Jedi. Later on, Vader may not feel that as strongly, but by then his anger has turned toward himself for failing to save Padme. He may feel that a man as terrible as he does not deserve to be "rescued" from the dark side, leading to a feedback loop where he only gets further enamored with its power and does more evil things which causes him to hate himself even more, and so it goes.
Answer: Anakin was seduced by the emperor to think that the Jedi were evil. This was partly fueled by anger &fear, thinking Padme would die if Palpatine didn't help save her. After he turned to Darth Vader & joined the dark side, he eventually realised the true nature of the Emperor, but he was to weak to do anything about it. Darth Vader still wanted to rule the galaxy, but didn't want the emperor controlling everything. He just wanted to use Luke to help overthrow the emperor and take over the galaxy. It wasn't until he found out he had a daughter also, and saw Luke about to die by the hands of the emperor, that he realised that Luke was right & he needed to switch sides.
Vader was not just using Luke to kill the Emperor. He actually did want to rule the galaxy as father and son - if Luke would turn to the Dark Side, that is.

Question: I'm confused. Palpatine wanted to use Queen Amidala to get himself voted as chancellor so he could have control over the republic. Why did he send Darth Maul after the Queen's ship when it escaped if he needed the Queen alive?
Answer: The entire time Palpatine is bitching to Viceroy Gunray that he needs the Queen to sign the treaty to make the blockade and invasion legal. He didn't send Darth Maul to kill Amidala, he sent him to capture her and to deal with her Jedi escort.

Question: When Anakin and Padme get married, Anakin is wearing an outfit that is often seen on Jedi and is displaying a Jedi Padawan's hair braid. Do he and Padme not care that the man who performs the wedding is seeing him (as Jedi are not supposed to have relationships and marry)? Why not disguise him? It's a huge risk to let even one person see a Jedi getting married.
Answer: Agolerga, who officiated the wedding, would have known who both people were, especially Padme. Remember they were also keeping the marriage secret because of Padme's position as Senator. Assuming Agolerga was aware a Jedi can't marry, he may simply not care or agree with the rule. Also, as a holy man of Naboo, Anakin and Padme may have trusted him with their secret.

Question: When Kylo Ren tries to use the Force on Rey, he mentions that they need the last piece of the map, and that they have the rest. However, when R2-D2 wakes up, we find out that he had the map the entire time. Was Kylo bluffing or did he know where the rest of it was? Was there a copy or did I miss something?
Answer: The First Order already has the piece that R2-D2 was carrying as well. That is the first piece, the large piece of the map missing a small section. The second piece is carried by BB-8 and only by BB-8, the missing piece in the map. All the first order needs is that second piece, and so does the Resistance. However the Resistance needs R2-D2 to activate again so he can show them the first piece, so they can put the second piece in it.
Answer: The piece of the map that R2 had was also recovered from the archives of the Empire.

Question: How did Palpatine come back? Cloned? Or somehow survived the Death Star explosion, which seems unlikely.
Chosen answer: According to the novelization, Palpatine sensed Vader's internal conflict and created a clone as a backup in the event that Vader betrayed him. When Vader threw him down the shaft, Palpatine transferred his consciousness into the clone's body.
Answer: It is not said exactly how he came back. He says that he had died before which presumably is him dying in ROTJ. The most we get is the reference to Sith ability that some consider unnatural.
It is not said how he came back, but I get the idea that he was using the Force to keep himself alive. At least that's the message I was getting when I saw that Palpatine's fingers were wilted away. And I thought that the power he was using was urging his life to go on, but his physical appearence was being dragged behind.
Answer: The line "The dark side is a pathway to many abilities some consider to be unnatural" is a direct reference to Star Wars Episode III: Revenge of the Sith, in which Palpatine says the same line verbatim to Anakin. Recall that a major plot point to that prequel is that the Sith have long been rumored to have found a method to cheat death. This film strongly suggests that Palpatine had indeed discovered this method. The film doesn't go into specifics. My understanding is the novelization says his body is a clone. Going by his appearance in the film (blank eyes; body manipulated by machine), it suggests to me that he is a reanimated corpse.

Question: I don't understand why Kylo Ren killed Han in the previous movie, but now says that he didn't hate Han?
Answer: As he says, "let the past die. Kill it, if you have to." Han was his past - he didn't hate his father, but his existence was holding Kylo Ren back from reaching his full potential, or so he believes. The principle is demonstrated earlier in the movie when he can't bring himself to kill Leia, but has no issue with the other TIE pilots blasting the bridge and (he thinks) killing her. He wants to free himself from the shackles of his parents, who cause him such internal conflict. Remove the source of the conflict and he believes he can move on to greater things. Of course, arguably his position is a bit naive, and his actions will actually cause him greater problems down the line.
Answer: As we saw in Episode 3, with Anakin Skywalker, turning to the Dark Side profoundly changes one's loyalty to friends and family. Anakin murdered children and nearly murdered his pregnant wife and his lifelong mentor. Kylo Ren seemed to follow the same path on the Dark Side, murdering his father.
Just pointing out that in Episode III Anakin did kill Padme, just not immediately. She gave birth to Luke and Leia and then died.

Question: 3 questions: Was the planet Krennic goes to to talk to Vader supposed to be Mustafar? If so, why would Vader want to go there of all places? Lastly, what was the reason Krennic went to visit Vader?
Answer: Yes, Pablo Hidalgo from the Lucasfilm Story Group confirmed Vader's palace was on Mustafar. Gary Whitta who wrote the story, suggested that he lived there because "he wants to punish himself" for turning to the dark side. Krennic visits Vader because he wants him to arrange a personal audience with the Emperor and cut Tarkin out of the equation.

Question: Did C-3PO and R2-D2 appear in this film?
Answer: I was wondering about this, too. C-3PO did not appear in Solo, and I cannot find any Internet reference pertaining to R2-D2 being in it. Curiously, Anthony Daniels, the actor who has played C-3PO in all the other Star Wars movies, makes a cameo appearance in Solo as another character (Chewbacca's friend).
Chosen answer: He "searched his feelings" as Vader instructed; he reached out with the Force and felt the truth of the statement.
Phixius