If the abuser has been convicted of a domestic violence misdemeanor or felony, can s/he legally keep or buy a gun?
No. Under federal law, if the abuser has been convicted of any felony or a domestic violence misdemeanor, s/he can never legally have or buy a gun.* Please talk to a lawyer who is knowledgeable about federal gun laws to find out if the abuser's gun can be taken away based on your specific situation.
* 18 USC §922(g)(1),(9)
How can I find out if the abuser has been convicted of a domestic violence misdemeanor or felony?
Domestic violence misdemeanor and felony records are open to the public, but they are not always easy to access. If you know the exact courthouse where the abuser may have been convicted, you can go to the courthouse and ask the clerk of court for access to those records. If you know the county where s/he may have been prosecuted, you may also be able to contact the county prosecutor to ask for specifics about his/her conviction.
Domestic violence misdemeanor and felony records are also kept in the National Instant Criminal Background Check System (NICS). However, only law enforcement officials and licensed firearm sellers are allowed to search the NICS. Your local police department may be willing to search NICS for you if you ask, but they are not required to do so.
To read more about the NICS, please see the question, What will happen if the abuser tries to buy a gun when s/he isn't supposed to?