The general answer is no. That is, if this is for a form N-400 naturalization application, not to remove the condition on your permanent resident card. In fact, you are given a second chance to take the naturalization exam before you must pay the filing fee, again. If you have sufficient documentary proof of your marriage, then you should be okay, but you should discuss the situation with an experienced immigration attorney, where there is a marital separation.
As long as you and your wife were in love and living together before the break up, the USCIS is usually going to recognize that spurned spouses can be vindictive. Occasionally, some marry in violation of criminal law solely for immigration purposes; such marriages can result in rescission, deportation and a permanent bar to immigration as a matter of law unless the USCIS cannot confirm fraud.
The above is general information; it is not legal advice. It is always wise to seek counseling from an experienced immigration and visa attorney.
No one is required to become a US citizen. You can remain a legal permanent resident forever. Your current card needs to be renewed in 2012, sort of like renewing a driver's license. As long as you are still eligible (you aren't a criminal and you can afford to file the petition) you will get a renewal.
You should get your citizenship for many reasons. Citizenship offers many protections and benefits not available to non-citizen residents. You could petition for family members to get their residence in the US, you don't have to pay to renew your greencard. If you do commit a crime (unless it was related to illegally obtaining immigration benefits) you are not going to be deported or lose your citizenship (but you could be deported if you are only an LPR).
Secondly, contrary to your wife's assertions, she isn't the US government and she doesn't have the right to deport anyone. That right rests squarely with our government and they are not going to exercise it on law abiding legal permanent residents.
Finally, you are not going to fail the citizensip test. First, you speak English. Clearly you can read and write. Even with the new tests, they are probably only going to ask a few questions (maybe 10) from the 100 or so sample questions. You can get free guides to the test online at www.uscis.gov. These are very basic questions about our government and our history. I'm sure you will do fine.