If your character is a normal vampire, can that mean that not only can I kill dawnguard people, but also members of the vampire faction as well, as long as we never joined the faction?

If you mean can you kill the Volkihar in the questline while being a Vampire Lord without doing the questline, I'd say no.

I never said anything about being a vampire lord, i meant normal vampires. Since i have a character that is already a vampire, is he allowed to kill members of both factions?

Who knows? It may be possible. Vampires kill each other all the time in games and lore.

as long as they're not essential you can kill anyone regardless of who they are...thats like saying can a nord guard kill another nord guard

Yeah, I don't get how it could be impossible for a vampire to kill a vampire. Except for people marked as essential, of course.