My question is, does moving fast while crouching/sneaking give me away more?
Yes, until you get silent running.
Am I better of holding the shift button while crouching/sneaking to better maintain surreptitiousness?
There's a toggle run/walk key you can map. Easier then holding shift.
Also, does mean that getting the "Silent Running" perk (Running no longer factors into a successful sneak attempt.) will let me just run without being detected
Let's you move quickly in sneak.
You are the most stealthy when you're not moving and not holding a weapon. Before you get silent running. Move slowly and don't have a weapon in your hand. After you get silent running you can sneak quickly and hold a weapon.