Combining your 2 questions, if you do do a warm up on the road rather than on the trainer, bring a spare tube with you on the warm up and make sure you stick close enough to the start line to always have time to fix a flat and still make the race start.
Better yet, bring a spare set of wheels even if their is not going to be a wheel car or wheel pit. a lot can happen to a wheel between home and the start of a race, not just in the race. As a grizzled Cat 1 vet said to one of my Cat 5 teammates after he broke a spoke 10 minutes before the start of a road race “anyone who shows up at a bike race without a spare set of wheels obviously does not give a shit about racing…” Acquiring an extra set of wheels should be on every newbie racer’s list as they move into the sport.