Can a player Move on to the touch line with the ball?

YES, but the opposition will receive a line out on the space where he crosses the touch line.

If I move a player, i.e. a forward, 3 spaces and then I move another player can I still move that forward his remaining 2 spaces?

NO. If you move a player and then move another, you can not return to the previous player and finish moves he had left over. Unused moves are lost.

Can a player move over or stand on the space occupied by the rugby pole?

NO. A player can not move through or onto the space occupied by the pole uprights. He CAN move through or onto the spaces occupied by the crossbar.

Can my player Move on to a grounded player, play a Safe Hands card to Gather the ball, and then Move off the player?

YES. As this player can not fail the dice roll for the Gather, he therefor runs no risk of ending the turn on top of the grounded player, so this is technically a legal move.