A. Anything is possible, just it would need to be a late flight out on Sunday afternoon to give you that 24 hour no fly time.
B. Probably Raleigh as that is the best bet to get to either Morehead City/ Beaufort & to Wilmington.
C. If diving in MHC/ Beaufort, most likely you will be diving with either Olympus or Discovery & they both have Bunkhouses. In Wilmington you will need a hotel room.
D. Discovery or Olympus in the MHC area, I also like Atlantis Charters, but Bobby & Renate only do 6-packs & their charters are normally filled way before then. An awesome choice if they have a spot open though. You would be then open to needing a hotel room & that time of the year it will be big $$$ in that area.
In Wilmington, Aquatic Safaries, big boat, friendly & very good crew, nice shop. Several hotels in the area, I stay at the Suburban Lodge on Eastwood, less than 10 minutes from boat & shop.
E. Signature dive would really depend on your experience & comfort zone. MHC you could do the U-352, not really known as a sandtiger hangout, but I've seen them there, What was formally called the Papoose, which is actually the Hutton. Normally lots of Sandtigers. There is also the Shurz & Spar which are both good dives with Sandtigers aplenty normally.
In Wilmington the more advanced sites are the Normannia, City of Houston, Rosin wreck & 18 Fathom Wreck. All in about 100fsw more or less. Maybe something shallower with plenty of Shark action would be the Hyde/ Markham.
Now if you want to be more adventurous there is also Cape Hatteras N.C., pretty blue warm water, but hotels will be outrageous $$$ & getting there from Raleigh would also be more of a hassle, but it is nice, with Outer Banks diving or Capt. JTs running ops out of there.