The aerodynamics of it all, are too complex to cover in one post
(or thread)(or entire forum).. but you've got a good grasp on the basics.
You can turn (change heading), by rudder alone, but as you've "seen", it's awkward and inefficient. Yawing will point the nose, hence redirect thrust, so you end up with a new heading.. but you're fighting the tendency of the airplane to want to fly straight and level, like fighting a "weather-vane".
When you turn by banking, you're redirecting lift, so the airplane happily "flies" toward it's new heading. Compensating for the loss off vertical lift by elevator, is also part of coordianting a turn, as can be adding power for extended, steep turning.
Rudder use is as much an art, as it is a science. And the turn-coordinator is used at first by students, as a reference. You'll soon develop a feel that's even more accurate, because a pefectly coordinated turn, is not always a centered ball.
Now.. as you first enter a turn, you'll experience "adverse yaw". This is the tendency for the nose to yaw a bit, in a direction opposite the turn... Once the turn is established, perfect coordination could very well be with no rudder input at all.. depending on the airplane, its airspeed, its weight and current CoG. During a climbing turn, it can take OPPOSITE rudder to coordinate it all.. and remember.. elevator and thrust are variables too.
A maneuver designed to help illustrate the adverse yaw, is called , "Dutch Rolls". It's the act of banking left, then right (repeatedly), while using the rudder to keep the nose pointed at a fixed landmark.
So.. in summary.. you'll use the rudder as you enter a turn to counteract adverse yaw.. and then use it (or not use it) for coordination, dependent on all the variables mentioned. Even in the sim, you'll end up getting a visual feel for what's a good turn, and what isn't.. and rudder use will become something you do without thinking about it..
"Heals on the floor" are for takeoff and landing. You don't want the brakes applied as the wheels first touch pavement.. and you certainly don't want to be dragging the brakes as you're buildin up takeoff airspeed. Applying wheel brakes in flight is harmless.
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