As I understand it, shipping firearms must be done through a firearms dealer, shipped to a firearms dealer at or near your destination.
I’ve shipped a pistol to Ruger and a rifle to Rock River Arms. Both companies sent me prepaid shipping labels. I dropped the pistol at the local UPS Store. The rifle, I had to actually take to a specific UPS office at the UPS facility. That was a requirement of RRA...they’d sent a list of very specific instructions. Both places, I was given a receipt. I’m in NC, so maybe there’s a difference between states?
Not necessary, my dealer says to ship my Remington to Remington. If you go to their website they provide detailed instructions. Now it's just a matter of getting it done...
You can always ship a firearm in your checked luggage. Just let the agent at the front desk know anf fill out some paperwork.