yes a one stroke penalty
You have made the distinction between, in the hazard and outside of the hazard, because of course, you can not ground your club in a hazard. If you address the ball but step away and take a practice swing there is no problem. You only incur a penalty if you knock the ball with the club and it moves. Also, a stroke is only deemed to have taken place if you make a genuine attempt to hit the ball.
No, you are not allowed to do so, you must not rake the bunker or smooth sand over with your feet, as this is deemed to be improved your stance or testing the ground conditions. You will get a two shot penalty for testing, if you do so.
When you 'ground' your club you have caused your golf club to come in contact with the ground or another substance such as water, sand or weeds. Generally speaking the subject of grounding a club centres around hazards where you are not permitted to touch the surface or the weeds that exist within an area marked as a hazard. If a player grounds their club in any of these examples they are penalized two strokes for doing so. If a player grounds their club on the putting surface and the ball moves - by gravity, wind or anything else - there is a penalty for this as well.
Yes, you may do so, the key distinction that you have made in the question is the ball 'out' of the bunker. If the ball is still in the bunker you would be penalised two shots for grounding a club in a hazard. If the ball is no longer in the bunker you are in you may ground the club, but be aware, there is really no need to.
playing a ball with a club from the teeing ground into the hole by a storke?
No its not because it shouldn't be there
No, you are not allowed to ground your club in the bunker unless you are taking the actual stroke. If you ground the club in a practice swing or prior to taking the stroke it is a two shot penalty.
Yes, this is allowed under no penalty. Even if you knock the ball off the tee accidentally with your club there is no penalty, it can simply be replaced on the tee.
Grounding the club means actually touching the club to the ground when the ball is in a hazard. The club cannot touch the ground until you make you swing.
When you hit the ball twice in one stroke, you must add a penalty stoke. Which makes that original stroke become two.
I am almost positive its when the club strikes the ground and pulls up grass and dirt and that kind of stuff.
Under normal circumstances, with your ball in the sand, if you touch the sand with your club and are not in the process of making a stoke (the downward motion of the club with the intention of hitting the ball) you incur a penalty for testing the sand. But since Tiger's ball was NOT in the sand when his club hit the sand he was not penalized. I think...please correct me if I'm wrong.