Having come into the province (epibas tēi eparcheiāi). Second aorist active participle of epibainō, to set foot upon. Literally, “Having set foot upon his province.” Eparcheia is a late word for province, in N.T. only here and Act 23:34. Judea was not strictly a province, but a department (Page) of the province of Syria which was under a propraetor (legatus Caesaris) while Judea was under a procurator (epitropos).
After three days (meta treis hēmeras). So in Act 28:17 in Rome. That is on the third day, with a day of rest in between. Precisely the language used of the resurrection of Jesus “after three days” = “on the third day.” So by common usage then and now.