I have a DVRO against the abuser. Can s/he keep a gun or buy a new gun?
No. California state law says that if you have a DVRO against the abuser, s/he cannot have a gun in his/her possession, or buy a new gun while the order is in effect.1 This applies to ex parte (temporary) orders as well as orders issued after notice and a hearing.2 However, there is an exception to this law if the abuser uses a firearm for his/her job. See The abuser uses a gun for his/her job. Do the state gun laws still apply? for more information.
Also, federal laws, which apply to all states, restrict an abuser's right to have a gun if you have a final protection order against him/her that meets certain requirements even if the judge does not specifically include on the order that s/he cannot have a gun. Go to the Federal Gun Laws page to get more information.
1 Cal. Fam. Code § 6389(a)
2 Cal. Fam. Code §§ 6218; 6389(a)