Days 1-2: Cairo
Pyramids, Sphinx, Grand Egyptian Museum, Old Cairo or a Nile dinner cruise depending on arrival time.

Seven days in Egypt can cover Cairo, the Pyramids, Luxor, Aswan and a short Nile cruise if the route is planned carefully.
Pyramids, Sphinx, Grand Egyptian Museum, Old Cairo or a Nile dinner cruise depending on arrival time.
Fly or train to Luxor, visit Karnak and the West Bank, then continue by Nile cruise or private route.
Finish in Aswan with Philae and optional Abu Simbel, or adjust the route for Hurghada beach time.

Yes. Seven days is enough for Cairo plus Luxor and Aswan if transfers and tours are planned efficiently.
Yes, but it requires trimming the Nile or Aswan portion. A better beach itinerary is usually 9 to 10 days.
Yes. The route can be adjusted by budget, hotel level, pace, guide language and preferred transport.