Yes you can kick a touchdown. By kicking an onside kick recover it and return it for a touchdown.
That would be a foul, you have to use the racket to return the ball.
Well, you can, I guess. But I would advise that you don't to because it might hurt a little.
Yes, you can kick a basketball.
Fun games played by children where kicking balls is involved could include Kickball and soccer. Kickball is a fun kids game very similar to baseball, but instead of a baseball and a bat, you use a gym ball and your leg to kick the ball and run the bases. Soccer is played in a long field where only kicking is allowed, hand contact with the ball is not permitted.
Let's play tennis! A good way to recognize prepositions is to imagine a tennis net. Now think of a tennis ball as a preposition (e.g., the ball can go "through" the net, the ball can go "over" the net)
Depends on what you mean by "you." I'll assume that you mean either a ball you have just hit, or yourself. If the ball touches the net on a serve, and bounces over the net landing in-bounds, then it is called a let, and acts just like a redo. If the ball hits the net and falls back on your side, then it is a fault and you loose the point. Any other time, the ball is allowed to hit the net. If you touch the net yourself (either with your racquet, clothes, body, hair) before the ball has bounced twice on the opponent's court then you loose the point.
Soccer tennis is when you have a tennis net and you volley a soccer ball with your feet over the net to the other player. Whoever messes up or hits the net losses a point.