My Nokia X200 fell down and the other moment the phone restarted.
Now only the hands Nokia symbol comes up and phone goes blank for 3 seconds and reboots again.
Is there any way to fix it at home like software updating or something
The phone is 3 years old and out of warranty.
Updating wouldn't fix anything, since what you're describing sounds a lot like physical failure.
The drop might have knocked an internal connection loose. It would need to be professionally repaired in this case. Though, if the phone is three years old you should look into upgrading to a new one anyway.