Yes, it is part of your equipment.
2 shot penalty
The question is unclear. If you hit your shot and it bounces off the cart path and goes OB then it is unfortunate, you must replay a shot from that position as you would do with any shot that went OB. If you are on the cart path, you should check local rules. Some courses have cart paths as an integral part of the course and the ball must be played off them, if this is the case you can play a shot off them or take a PENALTY drop. If you are allowed relief then you may take nearest point of relief (no nearer the hole) and one club length.
You have to take a penalty drop, which is one shot. So if you start a hole, and hit your tee shot into the water, you take your penalty drop and then play your approach, which will be your third shot.
Yea
Two shot penalty, he must replace his ball and then you must play your own.
You are given a two shot penalty in stroke play, or loss of hole in matchplay.
You pour the sand into your divots after you have hit.
If you hit your OPPONENT, HIS CADDY or PLAYING PARTNER or THEIR equipment there is no penalty. You can either cancel that shot and replay it from the original position or play the ball as it lies, your decision.If you hit YOURSELF, CADDY or PLAYING PARTNER, or YOUR equipment, there is a two shot penalty.
The penalty for hitting out of bounds is one shot, and you need to play another shot from where you played the original, so effectively it is two.If you hit you tee shot, 1st shot, out of bounds, add one stroke penalty, 2nd shot, them you are playing 3 off the tee, and therefore 4 from the fairway or rough.
When you hit the ball twice in one stroke, you must add a penalty stoke. Which makes that original stroke become two.
The key thing is, if you are playing a stroke and hit the tree then continue your swing and hit the ball then there is no penalty. If you are taking a practice swing and knock a leaf off then one shot penalty.
If you are off the green, nothing, and play the ball as it lies. If you are on the green it is a two shot penalty and you must play the ball as it lies. So if you are on the green, and putt with the pin in, and it goes in the ball is deemed holed, but there is a two shot penalty.