As Emily said in her earlier post, generally we should provide a negation that states that "something doesn't HAVE to happen."
Applying that rule to question number one, we should write: "it is not necessarily true that most drivers are not good drivers."
That construction is unfortunately a bit of a mouthful, and the answers on pages 6-92 to 6-93 try to balance the strictly correct negations with ease of understanding. So, you may see some answers that simply add or drop a "not" to negate the original statement, but as Emily said earlier this will get you to the right answer the vast majority of times.
Number eight is a more complicated example since it is a conditional statement. It states that if we don't lose our rights (i.e. if we keep our rights), then we must protect them. We can also phrase this in the contrapositive by saying 'if we don't protect our right, we will lose them.'
To negate a conditional statement, we need to express that the sufficient condition will not always lead to the necessary condition. The answer on page 6-93 may be phrased a bit too strongly than what is needed. the negation of this statement may be better expressed as "Even if we do not protect our rights, we may or may not
lose our rights."
Number seven is interesting because the original statement only speaks of possibility. That is, it states that something could be true. You may describe this as a "soft" statement. The negation in this case will lead us to a stronger statement.
As for number 12, what you wrote is logically identical to the answer provided in the book. The only difference is that you constructed your negation without using the word "without."
The original statement informed us that giving a substantial contribution would necessarily imperil the endowment. The negation of this is simply that giving a substantial contribution does not necessarily imperil the endowment. Your negation communicates this idea as well as the answer on page 6-93.
Let us know if you have any additional questions, and good luck!