If the pitch is in the strike zone, and the batter does not swing, it is a "strike." If the pitch is not in the strike zone, and the batter does not swing, it is a "ball."
Yes it is.
The batter would be charged with a strike.
Yes, you are awarded first base. When a pitched ball hits the ground before reaching home plate it does not become a dead ball. You can swing and miss and it is a strike. You can swing and hit the ball and it is a live ball. If the ball bounces and then comes up over the plate it can NOT be a called strike.
This is called a ball, or a B.
A pitched ball can hit the ground before crossing home-plate. In most cases the batter would not swing and the pitch would be called a ball. But, if the batter decides the swing, the ball is still in play after hitting the ground and the batter may not hit the ball and receive a strike, or he may foul the ball, or hit a base-hit.
A pitched baseball that hits the ground is a live ball, therefore you may swing at it. If you miss, it is a strike. If you hit it foul, it is a foul ball. If you hit it fair, whatever play results is legal.
It is a strike.
If you swing and miss and the ball hits you, it is a strike and a live ball. If you swing and the bat makes contact with the ball and the ball hits you while you're in the batter's box, it is a foul ball and a dead ball.
It's a strike and you are not awarded first.
A strike out is when a batter has two strikes (times when they either swing and miss or don't swing at a pitch in the strike zone) and they either don't swing at another pitch in the strike zone, or swing, and miss (if they make contact, but hit the ball foul, it's not a strike out)