I was watching the Hellsing Ultimate and I feel like a lot of backstory on characters is sort of left out. I don't quite get the reason for Walter's treason and why does he want to kill Alucard so bad?
And how did Walter go to his younger form in the last fight?
You have 2 questions here, and so there are 2 answers to provide.
Your first question, Why did Walter want to kill Alucard, has little to no real revealed reasons. The Wiki article for Walter C Dornez Has one quote that offers Alucards belief why.
Alucard goes on to present what he believes is the reason for Walter's betrayal; his fear of becoming old and useless. To prove his abilities to himself, Walter desired to destroy Alucard, and allowed this obsession to consume him.
This however has one flaw, in that Walter planned to die regardless of success or not in the end. proving oneself to not be obsolete, but then becoming obsolete instantly afterwards is counterproductive. Why he planned to die is unknown, but it was guaranteed for reasons I will mention later. This means that this reasoning was not the truth when Walter attacked, but it may have been the reasoning when he began. It was heavily hinted that Walter began his betrayal when he was about 14 years old, and first witnessed Alucard's power. It could be that he had that kind of reasoning at that time, but later on changed his mind, wanting to surpass or kill Alucard regardless of his death after success. That would satisfy half of the origional goal of beating Alucard, and in his older age allow him to die, at least satisfying his obsession.
It could also be that he saw Alucard as a real monster, a threat, and decided Alucard had to die, one way or another.
A third reason is hinted at by one of his quotes
"We are the evening's entertainment. And I... just wanted to do something with my time on the stage worthy of applause..."
if this one is the truth, it could be that he did have an obession with killing Alucard, but it was so that he could have the Legacy of being the one who killed Alucard the Neigh immortal and undeniably evil monster, to feel that his life truly had meaning.
We never truly got a straight answer out of him though, So this will probably forever be shrouded in that mystery unless someone else has stuff I missed.
As for your second question, How he got younger, it is a fairly simple one. He had the Millennium Doctor perform a special version of the Vampirification Surgery on him. He became an Artificial Vampire , and what made it special was that it's modified but flawed regeneration regresses his body as it activates. That tidbit is hidden in the wiki in the third paragraph of Walters Millennium Secret weapon part of his history Section. The down side was that it was not a perfected surgery, and was rushed, so permanent damage was done to him. He was literally deteriorating as he fought Alucard. His deterioration would cause his Flawed regeneration to kick in, and he would heal, and regress in age. As such, the surgery doomed him to only have hours or days left alive, no matter what he did.
While I cannot completely answer your question, I can point to a few reasons.
1) Walter is getting old, and he does not wish to.
2) Walter does not want to become obsolete.
3) Walter wants to defeat Alucard in battle.
Based on this, we can come to a possible answer. After Walter and Alucard fought against the Nazi in the Second World War, Walter saw Alucard as a challenge. He wanted to become stronger than Alucard, and thus made a deal with Millennium. He would be made into an artificial vampire, and try to kill Alucard.
The first comment mentions how Walter already planned to die after he killed Alucard, and then goes on to use the quote "We are the evening's entertainment. And I... just wanted to do something with my time on the stage worthy of applause..."
Based on these words, Walter wanted to do something that everyone thought to be considered impossible to become infamous. And as we see in the fight between Luke and Alucard, everyone thinks Alucard is immortal. Luke tried to prove otherwise by killing him but he failed, so Walter stepped in to prove what Luke Valentine could not. "Worthy of applause." He wants to do something he will be praised for, and he believes killing Alucard will get him that praise. It would be something he would be remembered by. Alucard also says in his fight with him that he believes Walter was
Afraid of becoming old and useless. Maybe [he was] afraid of being forgotten.
I don't think he originally planned to die, seeing as his betrayal started when he was fourteen years old and he had his whole life ahead of him. But as time passed and Walter grew old, he grew bored of life and was ready to die. So he planned to die after he killed Alucard, which was his life's goal. Or perhaps he did want to die after he killed Alucard no matter the age, and felt as though after he had completed his biggest goal in life, there would be no point in living. There's really no clear reason why Walter planned to die, so those are just a couple of my theories. But he betrayed the Hellsing organisation for a couple of reasons. As Alucard says, he didn't want to be old and useless. Walter also confirms that Alucard's theory that he didn't want to be forgotten. He just wanted to do something he would be remembered by. Everyone wants to be remembered for something great they did, and Walter is no exception.
As for him becoming younger...well, I believe that question has already been thoroughly answered, but I'll give a brief run-down of it.
Walter becomes what is called an Artificial Vampire (https://hellsing.fandom.com/wiki/Category:Artificial_Vampire That's the article. Forgive me, I don't know how to put the name with the link. I'm new to this website and this is my first time answering a question. Until now, I've just been reading threads.) Artificial Vampires are made using Mina Harker's DNA. Mina Harker is 'The Girl' who was mentioned in Alucard's dream in the second episode, and she is also one of the main character's in Brom Stoker's book. Mina Harker is special because she drank from Alucard (unwillingly), and therefore has his blood inside of her. (https://hellsing.fandom.com/wiki/Mina_Harker Wiki page on Mina Harker. I'll figure out this whole naming the link thing eventually.) The Doktor was using her DNA to make vampires, including Walter. He implied that Walter was supposed to be a higher level vampire by calling him an 'Experiment,' which he didn't seem to do with the other vampires he created. In this experimentation, he made Walter younger, and gave him advanced regeneration. However, since the experiment was rushed, it was flawed and also gave him advanced deterioration, as well as forced him to regenerate, which turned back time. (https://hellsing.fandom.com/wiki/Walter_C._Dornez The advanced deterioration is and forced regeneration is briefly mentioned in the 'Post-Experimentation' paragraph.)
So to sum all that up and put it in simple terms, Walter's body is being forced to regenerate, which is causing deterioration, and is shown in loss of years.
