-Do Dracula's vessels actually affect Dracula's powers and how?
Yes. His vessel has to be appropriate for his resurrection, or it will take too long to be perfect for Dracula to inhabit, and will make him vulnerable. Case in point: Curse of Darkness. Dracula's exclamation at his own incomplete transformation due to an imperfect vessel reveals that this is what allowed Hector to snatch victory.
I'm asking mostly because of that virgin girl from Rondo.
The virgin girl is not a vessel, but a sacrifice. While the vessel does technically qualify as a "sacrifice", Dracula's body is already whole by the time she is sacrificed for him. Hence, he's not wearing a meat-suit in Rondo.
-Is it possible that Galamoth is a vampire but we only see him in his monster form?
He could even be purely a man turned into a demon by his own will. Gergoth is this case: Cursed creation until he turned into a very powerful, monstrous creature. Brauner is another--turned into a vampire by sheer hatred of humanity. It's even explained (albeit possibly non-canonically) on that lost manga that Lament's Medusa was a human woman turned monster due to grief. So... yes-ish?
And given the fact that he has a Reaper I'm assuming he has a crimson stone? If anyone has any info on him (if possible from SotN, Judgement or other manuals) just drop some info please.
We know absolutelly jack squat about how the Time Reaper works, but Death knows that the Time Reaper is some kind of expy of himself.
The biggest assumption possible I can make is that the Time Reaper comes from chaos, yet is not a servant to the Crimson Stone. Otherwise why is it serving Galamoth and not Dracula -- the OG Crimson Stone owner?
Would it be possible for a Belmont to become Dracula's vessel, at what conditions and would Dracula then be able to use Vampire Killer?
Would not be possible, I believe. A Belmont (anyone, actually) has to be infused with Dracula's magic and succumb to his influence to be a good vessel, something the Belmonts are inherently immune to as per Order of Ecclesia's explanation -- Albus tried Belmont blood to control Dominus, but failed to realize that the property that allows the Belmonts to resist Dracula's influence is somewhere else. Mind control against a Belmont is another story, however**...
Even if he could possess a Belmont, he would not be able to wield the whip as it is holy. As per the Ricordanza novel, a character gets possessed by Death and, when he tried holding his generic holy whip, his hand burns, hurting him. That's just a generic holy whip, so imagine what the Vampire Killer itself would do. Probably make the possessed individual explode if they as much SNIFF it.
Crisis also said that this is essentially the plot of Belmont's Revenge -- it's not. Dracula is draining Soleiyu's power to make himself whole, and not "using Soleiyu as vessel" as in "inhabiting his body". Dracula turned into mist to escape the previous battle with Christopher, being too weak to turn back. His goal now is suck enough power from Soleiyu (that he gained by reaching adulthood) to enable his body to manifest again, not to use him as a vessel.
** The Belmonts are immune to Dracula's influence, and the difference between this and mind control is that the first reaches deep into your heart and corrupts your very essence once you give in, while the second makes you into a temporary puppet that can be awakened with a good beating. Dracula's influence cannot be easily "broken" like it happens to Richter or Soleiyu after a fight -- it ends in irreversible damage, more like Isaac, Albus or Barlowe. Even after breaking Dracula's Curse, Hector was STILL unable to free people from its effects, as Julia explains, and for you to see how deep this shit goes.