A kickoff puts the ball in play at the start of each half, after a successful field goal, and after a successful attempt. For a kickoff, a dropkick or placekick may be employed. A safety kick can be performed with a dropkick, placekick, or punt. A safety kick cannot be performed with a tee.
Yes, but it is considered poor form and should never be done as part of game strategy. While it is legal for teams in professional football to use the safety kick, they usually don't because it isn't in their best interest to do so. The safety kick only serves to cut down on points scored by reducing time left on the clock. There are no rules prohibiting this act per se, but it's generally not done because it is considered bad sportsmanship.
In college football, while still legal, the safety kick is extremely rare because most teams prefer to try for a touchdown instead. That being said, some coaches may choose to use the safety kick if they are in a close game and need to save time for other situations.
In high school football, the safety kick is also rare because most teams want to go for a touchdown every time.
However, it is legal in college football and high school football if there is an injury to any player on the kicking team during preparation for the kick. In that case, the opposing team may request to take over possession immediately before the safety kick is to be made.
Note: During a placekick on a kickoff, the kicking team may utilize a one-inch-high manufactured tee that has been permitted by the League. This allows for a higher kick than would otherwise be possible.
The term "kickoff" comes from the need to get the ball into play quickly when there is no opportunity for a free kick. Before the creation of the modern game, players could only take free kicks when the ball was out of bounds or their own end zone. Since there were no temporary goals, the only way to restart play was with a new ball in a new location. Thus the word "kickoff."
Today, most games begin with the coin toss, which determines who will receive the ball first. If it's heads, then you get to choose whether you want the receiving team to receive on offense or defense. If tails, then they get to decide. Either way you win, but it's important to understand why each side gets to make this choice. It's called "team orientation," and it ensures that both teams have an equal chance of winning or losing regardless of who they are playing against. This is very important in college football, where many games feature two relatively equal teams that might not be expected to meet in the standings.
The kicking tee cannot be repositioned once the ball has been put on it. The defending player must remain at least 1 yard away from the kicker while he is positioned in this way.
During a dropkick on a kickoff, the kicking team uses any object that is less than 2 inches high to kick off the ball. The defending player does not have to stay more than 1 yard away from the kicker during this procedure.
These are different procedures for different situations during extra points and field goals. See what works best under the circumstances to keep the opposing team from scoring.