If I qualify for a 4 yr scholarship, once my degree has been earned, do I get to pick where I'm stationed? How is that determined?

You'll go through a nation wide assessions process based on your order of merit list (OML) number. (It's were you are ranked and stacked against your peers at your school and nation wide). Unless you go to a Senior Military College, active Duty will not be guaranteed. Only thing guaranteed is Reserve component. Even if you are a scholarship recipient. You'll compete based on the above mentioned. If selected for Active Duty, they you will be assessed for your branch. You'll find this out your senior year. Your duty assignment won't come until you arrive for your Basic Officer Leaders Course. Bottom Line; GPA, APFT, and overall performance has a huge weight on getting what you want. Send me a line if you have questions. Good luck to you.

Engineering? If you choose/get to go Corps of Engineers, there's a follow on stuff at Leonard Wood and then assignment to your first position. Navy would start you at Pt. Hueneme, CA. What you heard about dream sheets, etc. is correct. It pays the body shop to meet the billet needs while pissing off the fewest number of MILs. During our basic school at "Port Whoneedsme" the flesh peddler showed up and pretty much assigned everyone their slots over a two day period. I did get a choice, Fallon NV or Antarctica. I took the later and that was one of the best choices in my life. Things are likely a bit different for you because you're a known accession in advance and they have to find a spot to get their investment back. Also pay attention to your path to professional registration as it will take a Masters to get there, especially if you're in the Engineering staff corps. The MIL side is good about making that happen as it is a pedigree requirement for O-4ish on up. Nothing like getting a full ride and pay to do grad school. I see Penn State is ABET certified in some of their disciplines so make sure the one you take is certified.

Not normally- needs of the service 1st.