Its a constant back-and-forth issue that of the second runway. But in all reality, LIM as it is now is too small for the traffic it currently holds.
For boarding passes - you may print them at the hotel but still may have to hop on line at the airport for a review of documents and weighting of bags. I'm not 100% sure (sorry!) whether it is as easy as dropping-off baggage and heading to the gate. Once with BPs in hand, if you find yourself with a bit of time, the area before security has good options for breakfast and sit down (e.g Starbucks). But not to worry as there are some quick options inside.