1. Yes, some dramas premiered while shooting others after filming. What genre do you like? Recent dramas like penthouse, hometown cha3x, vincenzo and goblin as well they premiered while shooting. While yumi cellls, hometown, jirisan, they premiered months after filming. It think it depends on the production company. I once read an interview of Gong Yoo he said he doesn't like shooting while airing kinda drama so he was hesistant at first to accept goblin. Something like that.
2. Yes, changing title is very common. Like The veil (black sun in korean), beyond evil(monster in korean), not sure why