Having come into the province (επιβας τη επαρχεια). Second aorist active participle of επιβαινω, to set foot upon. Literally, "Having set foot upon his province." Επαρχεια is a late word for province, in N.T. only here and Acts 23:34. Judea was not strictly a province, but a department (Page) of the province of Syria which was under a propraetor (λεγατυς Χαεσαρις) while Judea was under a procurator (επιτροπος).

After three days (μετα τρεις ημερας). So in Acts 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.