Not normally. Doing so would result in a 'turnover' (possession goes to the other team). There is one exception: when a throw is made and another on-pitch player (on either team) touches the disc but does not catch it, the thrower is allowed to reclaim possession as long as the disc has not hit the ground / another out-of-bounds object.
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No, if you have the disc in your hand you are not allowed to take a step, you only have a pivot foot. However, if you are in a full sprint and catch the disc, you can keep running while trying to slow down (known as momentum steps).
No, that would be considered a "travel" or a movement while not maintaining a pivot foot. Technically, you are maintaining a planted position, but if you hand-off the disc, then your teammate's body is considered part of yours and therefore is a travel.
A minimum of 1 by standard rules. Team captains may make special amendments beforehand and special tournament rules may apply
Your team keeps possession of the Frisbee by throwing it to each other. If your team allows the Frisbee to touch the ground then it is automatically a turnover to the other team.