Is it normal for the mother Cat to move her 3 day old kitten?

It depends on where the cat moved it, do you consider it safe? But you should never touch a kitten before it's eyes are open, unless you absolutely have to, because they are more prone to diseases when their eyes aren't open yet, talk to your vet and ask if it's a safe place and if not, then ask how you should move them or if you should touch them. It won't kill them but it's good to use precaution.