What is the normal movement in knee cap ( patella)?

Is it abnormal to only have up and down motion with no side motion at all? What if this is present with crepitus (grinding noises)?

Your patella should move up and down and side to side and also at slight angles. Patellas are surprisingly loose and move quite a bit. If you are having limited motion and a cracking noise it could be fluid in the joint, swelling, a patellar tendon pull or tear. Knees are tricky to disgnose simply from symptoms. If you are having pain see an orthopedist. Have a MRI and X-Rays. If you aren't having any pain or swelling I wouldn't worry too much about it, just be aware in case you do have some pain.

in an up and down direction

There are many more movements to the knee cap than simply up & down. Their is also rotation and tilting. The up and down motion is not a pure up/down motion as is goes in a groove so their is an arc pattern to the motion.

What happened to your patella, did you injure it?
Your patella should move in all directions (up/down & left /right etc).
If you hear grinding noise, you might have worn something out.
I would go see your doc. & have it checked-out before it gets worse.