Anyone can be turned into a vampire, but it takes a specific ritual to do it. One can do said ritual alone, but every year prospective vampires of the age of 20 are taken to a secretive location and transformed, in order to keep the tradition alive. Vampire lore is similar to that of Dracula, except that they can go out in daylight they just can't use their powers in direct sun, and they can be killed if their heart is removed, rather than if they're simply stabbed there. The wooden stake thing was made up as misdirection for vampire hunters in the early middle ages. Vampire families adopt four children over the course of a ten-year period of varying ages to turn, three men and one woman to be a bride to the eldest son, all generally from different families but there's no rule that says that they can't be from the same family and it isn't specifically frowned upon, it's just uncommon. The Frankensteins specifically go wayyy back, but they tend to kill their family members once they become the vampire version of senile/feral due to old age (bout 500 years old is considered old) in order to avoid disgrace. Vampires do in fact worship Satan, who they get their powers from.
Elizabeth, Victor, Ernest, and William are all from different families, with Elizabeth having been adopted in similar circumstances to the book. Justine is a werewolf servant, lower than the vampires but still with powers of turning into a wolf and while not immortal ages much more slowly once at the point of adulthood.
Biological vampire children are impossible, as vampires are undead and cannot procreate. Werewolves, on the other hand, can, and are often bred by vampires for the purposes of having servants so they don't have to do the dirty work of upkeeping their reputations and fabulous decadent castles.
Victor specifically wants to bring the dead back to life in a non-vampiric way with Alchemy, the way the old Alchemists used to. Good luck with that buddy.
Endgame is that Victor and Liz (and maybe Henry? Up to you.) both get turned into vampires, but refuse to marry (because they are SIBLINGS. Miss Shelley, they are sIBLINGS.) and flee together to avoid the shitty lifestyle vampires live.
Henry is a human, his father is a vampire lord and Henry is the second youngest male, Henry's older brother (EDIT who died previously, with his sister) is already a vampire and Henry himself is set to become a vampire like Vic and Liz. He doesn't want to go through it, but feels familial pressure to do so, his sister died and his family can't replace one so they're looking into marrying him off to a vampire widow (ew).
Does that help or do you want more info?