Hi mom2ethan! I don't live in Fayetteville any longer, but I grew up in a nearby community and also went to FTCC (for radiography) some years ago. I am however a nursing student and can try to answer some of your questions...
1. I really don't suggest any specialty of nursing, because I think you will find out which area of nursing is for you when you either rotate through your clinicals or if you are predisposed to a particular area of interest. Ex: Me personally, I love women's health. I've always loved women's health since I was a kid. I may find my niche to be OB or working for a GYN. I don't know for sure because I have yet to rotate through my OB clinicals. I have gone through one clinical rotation at the nursing home and two med-surg. clinicals. I have since realized that geriatrics is NOT my specialty, but I highly enjoy med-surg.
2. So far, I prefer the hospital. I like the pace of the hospital and the different kinds of patient problems I come across in the hospital. I know I am not interested in home health care because I don't want to go to different people's homes and not to mention the clientele for home health care is largely geriatric. As a nursing student, we will not get to rotate through a doctor's office as a clinical. I can't say I would be interested in working at a doctor's office because I think I would get really bored, really fast, (unless it was plastic surgery and I got to observe surgical procedures or something

).
3. I'm not sure if it would be hard to get hired at Cape Fear. When I was a radiography student, we had clinicals at Cape Fear, Highsmith-Rainey (downtown Fayetteville, I think they merged with Cape Fear and are called something else now), and the VA Hospital. From what I understand, it would not be too extremely difficult to get hired at any of the area hospital's upon graduation and getting your license. It may help to get letters of recommendation from your nursing instructors to submit to the hospital with your resume. It may also help in the hiring process if you worked there as a nurse's aide (PCA, or Nurse Tech) while in school?
4. I'm not working yet, but the hospital I am doing clinical's at is very flexible as far as scheduling. Schedule's are done monthly and there are always nurses willing to switch days with other nurses if they have a scheduling situation. Ex: the nurse that let me know this, works 2 12hr shifts and 2 8hr shifts a week this month. She doesn't have young children anymore but she said she enjoys working at this facility because of the scheduling flexibility.
5. My answer to this question is sorta tied into my answer to question #4.
I'm sorry to hear your degree is not lucrative in little ol'e Fayetteville. I can tell you once I get my degree I plan to move back to NC. If not in Fayetteville somewhere close, like Fuquay or a smaller city/town outside of Charlotte. My parents are still in Spring Lake on the Harnett County side, and everytime come home I hate leaving.
All the best to you and I hope my post helps. I'm sorry it's not all first hand info. I check the NC nurses forum every now and then and it's nice to see someone ask about Fayetteville instead of Raleigh and Charlotte.