If you are eligible to apply for citizenship is something else to consider, but regarding the criminal issues alone, the 2009 charge is within the statutory period at this time (within five years from the date you apply for citizenship) and in most cases would not be considered a moral turpitude crime, but at times can be considered a CIMT. The 2010 case is unlikely to cause a major issue by itself based on your description of the outcome, but there may be other ways it could negatively impact you especially since if you were charged with violating a restraining order (this means something happened where one was granted against you and that something or somethings could be issues that negatively impact your ability to prove good moral character). Working as a translator for the US forces will not really matter one way or another with regards to applying for citizenship (many people think letters from the military or affiliated agencies will help get them processed faster and/or get more favorable decisions, but they only help if you are already in a situation where your good moral character is questionable and they do not make the process any faster for anyone).
I would NOT recommend applying on your own just based on the criminal issues you have described. You need to consult with an immigration attorney or two to review your case and all documents associated and get a real assessment and real advice. It is in your interest to retain an attorney for your citizenship case.
Yes you can apply for citizenship. You must show good moral character for the five years immediately preceding filing the application for citizenship. The events in 2010 are not a problem you will need certified records for all arrests or court cases even if charges were dismissed or dropped. You may wish to hire an attorney to help.
The answer provided here is general in nature and does not take into account other factors that may need to be reviewed for a more precise answer. You should consult with an immigration attorney before taking any action. The answer here is not intended to create an attorney-client relationship.
I agree with my colleagues.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.