So I just talked to my recruiter today who is a young guy so he said he didn't have all of the answers...
Really? He didn't just guess?
To answer your questions... you
can do a masters in as little as a year, but it depends on a lot of things. If you start early enough, depending on the school, you can take some upper level electives that also count towards grad degrees (i.e., 5xxx level classes). Again, depending on schools and degrees, a lot of them require you to TA or something else, which is one reason it takes longer than a year (along with your thesis). Talk to a guidance counselor or a professor in the field you want to do a masters at your school, as you may be able to start credit towards it early.
As to grad school on a shore tour, I don't see why you couldn't do that and TPS, as long as you get the degree done quickly. I didn't know this, but like said, it has to be done before DH time, which is probably around the 10-12 yr mark (so 3 yrs flight school/FRS, 3 yrs sea tour, 3 yrs shore tour/masters, 3 yrs TPS/follow-on? not sure of the time... = 12 yrs). You might be able to shorten that shore tour before TPS if you apply and get in at the beginning of it, especially if you start the masters while on the sea tour (so you're done early on in your shore tour). Keep in mind, though, that any masters while on active duty will be a part-time endeavor (unless you do something like AFIT or Navy Post-Grad School), so it will probably take at least a couple years.
Like said, you can actually apply for TPS w/o a masters or tech degree. You can also apply for the joint AFIT (Air Force Institute of Tech.) - TPS program, where you get a masters followed by TPS, and do that instead of the shore tour.
Anyone with more experience on this, please correct any errors. Hope this helps regardless.