Questions (zētēmata). Plural, contemptuous, “a parcel of questions” (Knowling).
About words (peri logou). Word, singular, talk, not deed or fact (ergon, factum).
And names (kai onomatōn). As to whether “Jesus” should also be called “Christ” or “Messiah.” The Jews, Gallio knew, split hairs over words and names.
And your own law (kai nomou tou kath' humās) Literally, “And law that according to you.” Gallio had not been caught in the trap set for him. What they had said concerned Jewish law, not Roman law at all.
Look to it yourselves (opsesthe autoi). The volitive future middle indicative of horaō often used (cf. Mat 27:4) where an imperative could be employed (Robertson, Grammar, p. 874). The use of autoi (yourselves) turns it all over to them.
I am not minded (ou boulomai). I am not willing, I do not wish. An absolute refusal to allow a religious question to be brought before a Roman civil court. This decision of Gallio does not establish Christianity in preference to Judaism. It simply means that the case was plainly that Christianity was a form of Judaism and as such was not opposed to Roman law. This decision opened the door for Paul’s preaching all over the Roman Empire. Later Paul himself argues (Romans 9-11) that in fact Christianity is the true, the spiritual Judaism.