I cannot help with some parts of your request, but here are some ideas and some general suggestions..
I cannot help with homestays.
it is important to know what time of year you plan to visit. Snow at moderate to high altitudes can affect travel and activities in the winter. "Between seasons" find many facilities closed or shut down for annual maintenance, such as lifts to the mountain tops.
Also, do you plan any walking or hiking?
Land in Zürich.
Take train to Lucerne. Stay there or near there 2 or 3 days.
Visit lake, lake boats, any of Mt. Rigi, Mt., Pilatus, possibly Mt. Titlis.
Take the train to the Bernese Oberland (Jungfrau Region.)
Stay at Grindelwald, Mürren, or Wengen for a few days.
Explore the area, including possibly the (expensive) top of the Jungfrau.
Return to Zürich the night before your flight out. Stay near the airport, or, even downtown. (There are about 6 trains per hour to the airport, about 10-15 minutes away.)
I believe that Annika suggested you look atthe getting started section:
If you look at these other sections of My Swiss Alps, you can expand on those ideas.
Once you propose a specific or approximate agenda, we can add to it and refine it.