The line separating day from night
I am very old, but I won't disappear soon.
Indeed. You're as old as the rotation of the Earth itself.
Every day, I go through you, but you cannot feel me.
Yup - the dividing line passes right through us, but cannot be felt.
Some says that I am fictional, but I am visible.
The difference between night and day is an oft-used metaphor, but it is indeed a real thing and can be seen.
Only happy few really saw me.
... Of course it is really only visible from space, and only a very happy few have ever gotten to witness it.
I move, following the one path again and again, faster than sound.
The line moves around the Earth once a day, always following the same path, and travels well in excess of the speed of sound.
I am very fast and very slow at the same time, but I have always the same shape
Very fast, in that it travels over 1000 mph at the equator, but very slow in that it takes all day to finish its trek. And always the same shape - a line, moving in an orbit around the Earth.
You can see my fellow on the moon
You can also see the dividing line between the lit and dark areas of the moon, as it changes from full moon to new moon and back each month.
a famous character took my name
The dividing line between night and day has a name.
It is called the terminator.
There's also, of course, a very famous film (and its sequels) about The Terminator.