We hunted newfoundland, northern area (forget the zone, but east of River of Ponds) last year. Don't worry about the rut as far as activity. All Newfie outfitters average close t 100% regardless of time of the season. We went (and in a few more years will again) the first week of the season (roughly start week of 9-13) because it was pre rut, and we wanted to ensure the best quality untainted meat. Into the rut, and it definitely is affected.
Sorry cant comment on the weather, but like all big animals, they will be more likely to seek the cool areas during the day if warm. The guides assure us that ,more bulls are seen due to their movement during the rut, so it is your choice. We both got bulls, but due to foul weather didn't get very picky - we were very happy with palmated bulls the first huntable day, as the weather was going to deteriorate the rest of the week....but still saw 9 moose that day.