He had a softish spot for a handful of individuals and unlike many other Sith, Vader didn't generally kill innocent people for no reason - but he always hated the Jedi and he had no regrets about what happened to them. The best proof of this is how he throws himself into becoming the Empire's primary Jedi hunter.
However, when he found out that Luke was his son, that was when he started to regret his decisions. Vader became conflicted about the fact that he had a son. This was the first time he regretted his decision to turn to the dark side in many years.
The added risk Darth Vader takes in allowing children to live in a situation where he could have killed them proves that he regrets killing Younglings and will avoid harming any more children for the rest of his days, though intense intimidation is a dark strategy to avoid repeating his Youngling massacre.
In Star Wars: Episode III - Revenge of the Sith, Darth Vader slaughtered Younglings to cement his position as Palpatine's apprentice - but he was still haunted by this after The Empire Strikes Back.
The short answer is yes, without a doubt, Vader regretted becoming a cybernetic monstrosity. First, there's the constant pain and discomfort from his suit. Worse, however, is the psychological pain. Vader destroyed everything he had ever known for a chance to save Padme.
Giving in to his feelings, Anakin cuts off Mace Windu's hand, giving Palpatine the opportunity to kill him. Anakin regrets this almost instantly, but the thought of Padme was stronger than his remorse This is the moment Anakin officially became Darth Vader and led to serious issues in the Skywalker Saga.
It's not shown, but it is clearly insinuated that Anakin killed the younglings. This is confirmed later in the movie when Obi-Wan informs Padme that Anakin killed them. Both are torn apart with hurt and confusion, trying to make sense of something so terrible. How could Anakin do such a thing?
Emperor Palpatine viewed Darth Vader as a disappointment, and yet he let him live.
Although we never see Leia fully reconcile with the fact that Darth Vader is her father, it's worth noting she did actually forgive and accept the former Sith Lord in the non-canon Legends novel "Tatooine Ghost," by Troy Denning.
Yes, his entire character since then was a self loathing tragic monster who has little reason to care about anything. Betraying Mace Windu instantly made him regret his act of impulse, Padme's death and rejection of his actions later on made it stick.
Darth Vader hated Obi-Wan Kenobi because he hated himself. This started when he thought that Kenobi was the one that poisoned Padmé into turning against Anakin when he turned to the dark side. But the truth was that Anakin was merely projecting his own self-hatred toward Obi-Wan.
Yes, when Darth Vader turned back to Anakin Skywalker and sacrifice himself to save his son, he dies and Obi-Wan uses the force to connect with Anakin's spirit. In that time Anakin apologizes to Obi-Wan, desperately asking him to forgive him for everything he has done to him and everybody over the years.
If Vader was able to access his full potential and immerse himself completely in the force, he would have no trouble overthrowing Palpatine... So for that reason, Vader's suit kept him in a constant state of weakness, but also brought his his full range of anger and pain.
Despite his somewhat pure origins as a Jedi, Darth Vader definitely has plenty of moments where he genuinely enjoys what he does on the dark side.
For his disobedience, the Emperor punished Vader and resolved to teach him a lesson in the dark side of the Force, removing his cybernetic limbs and having him dumped on Mustafar by a squad of death troopers to either strengthen his Sith apprentice with pain or leave him for dead.
This is revealed in Star Wars: Darth Vader (2015) issue 20. After Mustafar had crippled Vader, Sidious assumed that Vader would never wield the level of power he once had. He thought Vader was a broken husk of a man with little to no use left. He wanted stronger candidates to enforce his rule throughout the Empire.
Emperor Palpatine should have known Darth Vader would betray him in Return of the Jedi, but he was blinded by his arrogance and ignorance. Palpatine couldn't predict Darth Vader's betrayal in Return of the Jedi for one simple, yet very powerful reason.
However, when they next met in Star Wars: Episode II – Attack of the Clones, Anakin and Padmé's feelings for one another grew into something resembling love, and their wedding at the end of the film solidified their relationship as one of the most important romances in Star Wars history.
However, when Palpatine destroyed the Republic, Panaka sided with him. Though he never acted against Padme, his support of Palpatine included the support of a stronger military presence, which was a betrayal of her ideals.
The Younglings Reminded Anakin of How Different He Was
Those negative emotions also power the dark side, meaning Anakin likely felt stronger as he killed the younglings. That, in turn, reinforced his belief that only the dark side could save Padmé.
The maverick Jedi Master Qui-Gon Jinn comes before the Jedi High Council, which Windu is a member of, and offers to train Anakin Skywalker, believing that the boy is the Chosen One of Jedi prophecy. Windu and the other Council members decline, deeming Anakin too old and full of fear.
He didn't. What people interpret as dislike, was actually fear. The reason Windu seemed so cold towards Anakin, was because he was afraid of what he could do. According to the Episode III novel, Windu believed that Anakin's powers were growing far too quickly, and that he was not disciplined enough to control them.
In Attack of the Clones Mace Windu actually regretted killing Jango Fett in the arena on Geonosis.