No. He only hints that they are more than they seem and likely in a paranormal way. He does this very indirectly by showing him something and allowing him to to draw his own incorrect conclusion. This occurs in Breaking Dawn.
Yes and no. Charlie had a mind shield that his daughter, Bella inherited from him, but hers was stronger. He never found out about the Cullens being vampires, but Jacob shape-shifted into his wolf form right in front of him. After that, he believed that whatever he learned would be on a need-to-know basis.
the beach doesn't have a name but it is in the quillute reservation in Washington
Bella found out that the Cullens were vampires by overhearing a conversation between Edward and his family members discussing their supernatural abilities and the risks involved in being around humans.
In Breaking Dawn, Irina betrays the Cullens by telling the Volturi about Renesmee, Edward and Bella's half-vampire daughter. She does this because in New Moon, Irina's mate, Laurent was going to kill Bella. Jacob and his werewolf pack intervene and kill Laurent first. Irina is still upset about this in Breaking Dawn, so she betrays them.
he gets freaked out
Her twin brother is Alec, and no they are not cousins with the Cullens. They're just compatible by being vampires.
A vampire is a mythical creature. In "Twilight" all vampires, are decribed as being pale skinned, fast, beatiful, having topaz/red/black eyes and very strong. Vampires are blood-drinkers. In the "Twilight" series there are other vampires expect from the Cullens. The Volutri for instance, they drink human blood while the Cullens drink animal blood. Some vampires have special powers while others have special qualities.
The fan fiction story Emancipation Proclamation is about Bella being sold as a slave to the Cullens. In the story everyone is human, so no vampires. It's pretty good. Hope that helps!
In "Breaking Dawn," the Cullens do celebrate Christmas. They have a tradition of finding a Christmas tree in the forest and decorating it together as a family. This shows their efforts to integrate into human customs despite being vampires.
because Bella is in a race against time with edward to save herself from being killed in revenge by some other vampires that are not the cullens
Some of the Cullens (especially Rosalie) were angry when Edward saved Bella from being killed by the truck in Twilight because he could have given their secret (that they are vampires) away, as he used his vampire strength and speed to save her, but he did it in public.
He is a half-human, half-vampire, who killed his mother being born, and helped the Cullens and the other vampires against the Volturi. Otherwise he is nothing else... :-)