Is there a mode or practice where you can explore the ark and just mess around by yourself or with friends like they do in the video in the airport where they explain smart?

Open a private match and disable the bots. Get your friends on the same team, turn off friendly fire, and just run around.

Not sure if mission timers can be turned off.

The Game seems like a fast pace shooter. To be honest I do think they will BUT I do think thats a cool idea!