If you use a Quest Trigger to start an Urgent Quest (for example, The Face of the Abyss Trigger), is there a limited amount of time for people to join the quest once you use the trigger or can you just sit there as long as you need to for the quest lobby to fill up?

the trigger after activated will be there for 1 hour however there's a time limit to people can join I don't remember how much time is but no you can't sit in the lobby and wait to fill up, if you do that you probably gonna lose the trigger.