score:4
To answer your questions in order:
You don't need to print anything. The App will automatically download a mobile boarding pass.
If you are checking bags, just go directly to the bag drop. Otherwise, go directly to security and show the mobile boarding pass. (If you have an iPhone, it will be in Passbook and already on your lock screen.)
Take a screenshot.
You can still print a paper one from the kiosk. Also, if you check bags, they will usually print one for you at the bag drop (to attach the bag info stickers to).
Upvote:3
For company reimburs*m*nt purposes, you can also print a passenger receipt, which is available online up to 30 days after the flight.