yes, every rider is in contention for a given checkpoint.

as for specific designated sprinters, no, there's no limit on who can compete for the points by tour rules. Now, teams have guys that are their sprinters and climbers and the rest of the team helps them out by leading (blocking the wind) and stuff. But if the newest guy on the ride wants to go for it from the back of the peleton, there's no rule that says he can't. There are, however, lots of etiquette rules in bicycle racing that apply and I can't begin to explain those - mostly because I don't know the politics of the peleton at all. Things like pee breaks, food issues, crashes and the peleton waiting for someone to rejoin, attacks when a leader takes a crash etc. Overall, it's a pretty "sportsmanlike" sport.