Does the Army do stuff like close order drill? Like in the Marines, with the marching and all that?

After basic and AIT, most units won't be practicing close order drills unless to practice for a change of command or event where they have to pass in review.

every service does close order drill, even the navy and coast guard

They do it to teach troops how to move a group in an orderly fashion, from one locatiol to another,

Probably. I like showing my penis to all the guys.

Yes. However it is little used unless you have a parade or some formal function to do. I bet a lot of wasting time right now practicing for Trump's parade.

Possibly