[APG]

Let's clear up a few things:

Steps aren't important when determining travelling under NFHS (high school) and NCAA rules. It's about establishing the pivot foot. Steps are only important under NBA rules. Also know that there are plays under NBA rules that are completely legal, but are not legal under NCAA/high school rules.

Also know that you can't travel unless you're holding the ball.

As for your last situation. I'm assuming you're trying to say that a player ends his dribble and gathers the ball while a foot is on the floor (we'll say the left foot)? If so, what can happen next depends on what rule set you're using:

NBA:

A player is allowed two steps after he has gathered the ball. The first step occurs after a player steps after he has ended his dribble. In this scenario:

1.) A1 may step with the right foot (step one), then step with the left foot (step two). In this case, the right foot would be the pivot foot.

2.) A1 may step with the right foot (step one), then jump off of that foot and land simultaneously with both feet (step two). A1 would not be able to pivot in this situation.

3.) A1 may jump off the left foot (the foot that was on the floor when the player ended his dribble) and land on both feet simultaneously (this is considered step one). Afterward, he may pivot with either foot.

Now let's take a look under NCAA and high school rules:

1.) A1 may step with his right foot. In this scenario, the left foot will be the pivot foot.

2.) A1 may jump off the left foot (the foot in which the player ended his dribble on, and land on both feet simultaneously. He may not pivot in this case.