Why does anyone in Forest town not notice that Edward is a vampire and he always remains 17? Do they keep moving from town to town to hide identity?
People in Forks don't notice that Edward is a vampire because in the Twilight mythos, vampires can walk during the day, they just become unbearably beautiful and sparkly in the sunlight. Luckily, Forks is one of the least sunny towns in the country so they can lead "normal" lives. When it's sunny, Dr. Cullen and Esme (the "parents") take the Cullen kids "camping" and they hunt for animals to eat in the forests.
When they start to age, the kids go to "college" and the Cullens move away to their other residence with other vampires like them in Alaska (before they irritate the Alaskians, but that's a another story for another time ;) and after enough time has passed, they could go back to Forks.
Well simply because these "vegeterian vampires" have chosen a more normal way of living(having made a house, earning money through their jobs,attending high school),simiral to that of normal people.They take all sorts of precautions by avoiding close contact with other people(they are admired by the Forks community,but don't have strong, friendly bonds),avoiding sunlight and eating animal blood in order to have a more natural eye colour.They are totally inconspicious.Pus they do move a lot and change places, either when somebody suspects them or when the kids are supposedly done with school!
It is not very sunny in Forks so they can blend in as if they are normal human beings and when they have to go camping they are actually going away from the sun so no one will notice. When it is time to go to college they travel somewhere far away like Alaska to lose contact with everyone else. Then they start a new life and no one will notice.