I have noticed that in Avatar the last airbender, everyone seemingly has to move a body part to bend an element. Do they have to even move? And why?
For instance, Katara can be on land and use a nearby water source so is there some psychic connection?
Yes, they do, except for rare exceptions, both in The Last Airbender and in The Legend of Korra:
Certain benders are able to effectively manipulate their element with very minimum bodily movement, such as only their head. In even rarer cases, it is possible to perform their bending without the aid of physical movement at all, instead using sheer focus and force of will; a skill known as psychic bending.
This is even the case for the Avatar in the Avatar State (probably because it is easier to bend this way), as seen in the last combat of Aang again firelord Ozai or when Kyoshi uses her metal fans to detach Kyoshy Island from the continent.
Usually, but not always. In legend of Korra we see a waterbender bending without using her arms, she doesn't even have arms.
No I disagree because when avatar Aang first tried to bend fire he started a fire that burned Katara, and that is when she discovered that water benders have an healing ability.
I believe you need some amount of movement, combustion man still needed to breath, bumi still needed to move his face muscles, thought doing it with minimal movement is an advanced technique
