Lethal damage and effects that say "destroy" won't cause a creature with indestructible to be put into the graveyard. However, a creature with indestructible can be put into the graveyard for a number of reasons. The most likely reasons are if it's sacrificed, if it's legendary and another legendary creature with the same name is controlled by the same player, or if its toughness is 0 or less.

If any creature leaves your control, it will retain indestructible.

Once Dauntless Escort's ability resolves, the set of creatures it affects is locked in. It won't affect creatures that enter the battlefield after the ability has finished resolving.