Voldemort's Fear of Death
Voldemort fears death, yes. He became immortal at age 16. So he must have been afraid of death long before that, for him to want to live forever. So before he made his first Horcrux, do you think he might have constantly worried about death? Like some constant nagging in the back of his mind that death was all around, and he could die any minute, by anything? Paranoid, even? I dunno, just a thought...
I think a certain amount of paranoia makes sense, but it in terms of it being characteristic, it really depends on how it's written.
Much of his fear of death comes from his fear of being ordinary. He didn't want to be normal, he wanted to be special, and he was very pleased when he found out he was a wizard.
He saw death as a weakness, since he saw his mother as being too weak to fight death.
How much did he find out about his mother and father? I know he traced his family back to Slytherin and found out where to find his family to kill them, but what exactly did he know about them?