How does the game avoid dead time in the setup for getting 100 people
to all start out at the same time?
When you click
Play Button you enter in a matchmaking queue, and a few seconds later you enter to a lobby, you can see at the top of the screen how many people are at the same time in that match, and you may wait about 30 seconds to start the game (appearing in plain).
Are there just so many people going from game to game that it's no big
Yes, in September 16th PUBG sets new Steam Record for concurrent users (related here) beating DOTA record set in March 2016.
Are there long wait times in a lobby?
No, over 30 seconds every match.
Do people who die early never know or care who wins the match?
No, it doesn't matter who wins the game, your mission is to be the winner of the game.
Are some people allowed to come in a bit late?
When the lobbying time is over, you cannot enter the game as a new player. In the event that you have started the game and the game is closed, you can resume the game as soon as you connect again (if you have not been killed before).
Is there any real community development as a result of game play itself, where players get to know each other in-game?
Ingame you have a Voice Chat with the people on your team (if playing in Duo or Squad) you can talk with them while playing.