YMMV. I told them I was only available for one location...the one close to my house. Wasn't a problem. Also, when I interviewed folks for Amazon, that was NOT one of the questions I asked. (In fairness, that question might be asked by the recruiter or HR).
"Too many 12 hour days"....yup....like every day. Holiday season (Peak) is the worst...16+ hour days 6 days a week, but it's all part of the "wonderful" experience.
Big 2 on the PMP. I've found it to be very helpful post-AF. However, I found the Syracuse program to be crap...didn't prep me to pass the exam. Some of it may be my fault for treating it like a CBT, but still. (The exam is no joke...don't expect to pass without a lot of studying). I did a 1-week Boot Camp for $2K. Passed the test first try. Consider the Boot Camp + $500 exam fee + yearly PMI membership to be an investment in yourself. PMP + MBA + military = $$$. (And having Amazon, Google, Facebook, Apple, etc on your resume/LinkedIn helps a lot as well).