In brief, the difference between civil liberties and civil rights is that civil liberties are freedoms from government interference in our lives whereas civil rights have to do with ensuring that the laws treat all groups of people the same. Civil liberties prevent, for example, the government from infringing on our freedom of speech while civil rights prevent the government from treating different groups (for example, men and women or people of different races) differently.
As to your second question, this is a matter of personal opinion. Different people would answer this question very differently. On the one hand, we could argue that security outweighs civil liberties significantly. We could say that no one’s civil liberties are more valuable than the life of another. Therefore, if the government has to listen to my phone calls and read my email to make sure that I don’t kill anyone, that is fine. If I have nothing to hide, I have not been harmed by the surveillance. By allowing it to happen, I help to prevent others from being killed.
On the other extreme, we have people who quote (or misquote) Benjamin Franklin, saying that “Those who give up liberty for security deserve neither.” In this view, when we give up our liberties, we have let the terrorists win. We have destroyed our way of life, which is just what they want us to do. In this view, if the government infringes on all of our civil liberties, it is a “cure” that is worse than the “sickness” of occasional terrorist attacks.
Then, of course, we have various intermediate opinions. To most people, the balance lies somewhere between these two extremes. For example, you might think that it is okay for the NSA to collect data on who calls whom as long as they do not also record the phone calls. You might think that it is okay for them to record the phone calls if they are between people who are suspected of sympathizing with terrorists. You might think that it is okay to have extra surveillance on all Muslims in the United States because they might become radicalized, but that it is not okay to violate the privacy of anyone else.
There is no way to specify exactly what the proper balance is. Most people would probably say that we should not give up much of our civil liberties unless we would gain a significant amount of security. However, it is very difficult to set out what “much of our civil liberties” or “a significant amount of security” means. How much of your own privacy would you be willing to give up in order to have a better chance of preventing terrorist attacks?