There is a lot there to look at. I’d recommend, if you are having trouble with a walk cycle, to just do an animation of the walk cycle on a loop, from the side, from the front, and from a 45 degree angle. Leave out the credits, titles, etc, etc… just the plain animation. And include frame numbers, too, so people can reference which frame they see something happening or needed.
Overall, two things contribute to a robotic look: lack of weight, and lack of secondary motion. I think you’ve got a sense of weight, but the secondary motion is a problem.
For example, a character, holding his arms out to the side, turns. His arms turn smoothly along with his shoulders. This looks robotic. A human’s arms would lag the shoulders by a certain amount. A sort of ‘rule of thumb’ for a walking character making a turn: the eyes turn first, then the head, then the shoulders, then the abdomen and hips, and finally the feet. Many beginners do it the opposite way, turn the feet first, and the rest of the body just sort of swings along with the feet, and it looks like an amusement park ride.
As to which types of handles to use: watch out for ease in, ease out (bezier). It’s very useful in its place (all the handles have their uses) but it should be a deliberate decision, generally when some motion is starting or stopping. Using ease in-ease out on a continuous motion key frame makes the motion look ‘floaty’. Other than that… use the one that looks good. You’ll have to experiment and get a feel for the type of motion each one produces, and make a deliberate decision to use the one you pick. All the handles are useful, even vital, in the right circumstances.