I do like LoS in general... but LoS 2 really dropped the ball when it comes to story. It's all over the place - does he want redemption, does he want death, does he want revenge? What was that "when the moment comes, choose your family" moment was all about? Why does Vampire Killer kill Satan? What were the Masks all about? Why does Dracula suddenly not want to die in the end? Why is Alucard okay with his hated father still being alive? What happens to them now? Who's going to manage hell now? What did Drac see in the mirror before he shattered it? What was the Castle? Was it a mental projection or a real place? If it's a real place, where does it exist? If it's a mental projection, how does he bring the bald guy in there and how did he meet Agreus? Why doesn't Dracula question modern technology? Why don't people question Zobek being still alive? Why didn't Zobek and Dracula thought, for just a moment, that the scary looking b[bleep!]tch may just happen to be an acolyte? And if Dracula can take on Death and Satan, why can't he kill a single Golgoth Guard?
I'll answer this case by case
1. He initially wanted death, but throughout the game he develops through interactions with Marie and Trevor (who represent his humanity), victor, and alucard into wanting both revenge against zobek for his role in Marie's death, and lucifer for his manipulation of the events themself. It's why Gabriel is quite happy to kill zobek In a more personal manner.
2. The moment is to remind Gabriel that, if he wants to one day be reunited with Marie and reconcil with Trevor/alucard, he needs to remain true to his original self.
3. The vampire killer, due to being forged by the holiest if blacksmiths and having been somewhat further empowered by zobek, is able to slay the weakened lucifer (who is weaker on earth than in hell) due to being a creature of darkness, just like the lords of shadow.
4. The masks were more of a red herring than a true plot device. Lucifer used zobek to cause the spirits of the dead to be unable to ascend to heaven, to deny god and to, likely, eventually use them to become even more powerful than his father. The gods mask idea of power was implemented into zobeks mind to further this, and he was given the devil mask to gain easier control over others as well. It was all to further lucifers goal.
5. He's been reconciled with his son, so he is no longer alone. And, with alucard and having grown past the death phase, he wishes to repent for his actions and redeem himself.
6. Alucard knows that only Gabriel would be able to defeat lucifer, and, since Gabriel has been in seclusion for centuries, has likely mellowed out and isn't as angry as before at his father.
7. They will likely try to protect humanity. Who is to say that only zobek and such were the only threats? Other vampires can rise, demons or beings from the shadow realm as well. Not to mention, lucifer died on earth, so he's still in hell.
8. Lucifer. He died on earth, not hell. He's always weaker on earth and will return to hell upon death or defeat.
9. Likely saw that he may be able to truly redeem himself yet. Likely a sequel hook though.
10. The castle is a pocket dimension itself. It is from where Gabriel can store his powers and the denizens of his castle, which explains how the castle itself quickly repairs itself once he's around. Gabriel is able to bring others into it and things out of it, which is why the blood can escape from it and how he can bring the bald dude into it. It holds his humanity and powers as well. As for agreus, he likely traveled into the dimension to take revenge upon Gabriel for pans death. Agreus was an old god as well, so he did have some power.
11. Because modern tech is easy to grasp outside of going into its insides. You don't need to know how a light switch works to realize that you need to flip it to turn the lights on.
12. Only Gabriel knew zobek had seemingly died, and even then, he did ask how he was still alive. Zobek likely had a way to avoid dying due to being The Lord of the dead.
13. Because she was, previously, just looking like a normal human who, when apparently exposed to the gas, was transformed. They thought that she was transformed and as such, wasn't an acolyte.
14. The guards armor is indestructible. But they are quickly grown grunts with the mind of a child. They are only useful to serve as basic guards, nothing more.