Do not be distracted by extraneous movements
The primary movement that should concern you is movement toward you, since it decreases range and may be an attack. Secondary is movement away from you, since it increases range and may affect your attacks.
Taekwondo is known as a kicking art, but it is actually a kick/punch art. Blazingly fast hands can score, intimidate, and set up kicks. Half the observed speed of a punch is not related to motion, but to the absence of motion. A punch may occur with no warning, pre-movement, or telegraphing.
Memorized combinations versus free-form
When sparring, you may use memorized attacking combinations or you may just go with the flow. If you practice a few attack combinations until they occur spontaneously, they may be effective against many different types of opponents. If you learn to "read" your opponent and react accordingly, you will become a much better fighter.