I'll answer the questions I have experience with.

Day 2
QUESTION: What would be best to see this day since we will be tired from traveling?
>> There are many things to see in the city of Cusco itself. The Museo Inka was one of the best museums we went to in Peru. They have tons of artifacts from the Sacred Valley sites (and more). If you feel up to walking, you could take a taxi to Sacsaywaman, Puka Pukara, Q'enko and Tambomachay. They are all on a hill overlooking the city.

QUESTION: So many hotel reviews...which is best? Looking for best locale, service, experience.
>> I don't know exactly what you're looking for, but we stayed at Piccola Locanda. Very cute, clean and all-around great place. The only downside is the hill plus stairs you have to climb to get to it.

Day 3: Tour Cuzco
QUESTION: What to see?
>> Sacsaywaman, Puka Pukara, Tambomachay and Q'enko are all must-sees in my opinion. If you want something a little less touristy, take a walk (not far) to the Cusco market. You can get a very cheap lunch/snack and see how locals shop.


Day 5-8: 4 day trek to MP
QUESTION: 3 people from our group will not be trekking, but will meet us in Agua Callientes to tour MP and hike Huayna Picchu. What should this group do while we are gone?
>> They should see some other Sacred Valley sites. They will need to take a tour, hire a guide/driver or hire a taxi. I recommend Tipon, Maras, Moray, Ollantaytambo, Pisac.

Day 9: 1/2 group will hike Huayna Picchu and half will relax at hotel. Leave for Cusco in afternoon.
QUESTION: Should we take a late flight to Puno or an overnight bus? Or just stay in Cuzco and fly out in the morning?
>> We took an overnight bus from Cusco to Puno out of necessity (there was a strike in another area of Peru which changed our itinerary). It was not pleasant. But we did not take one of the fancier bus lines. If you do take an overnight bus, use Cruz del Sur or Oltursa. Some other people on the forum might have more recommendations, but we had our best experiences with them. Bring ear plugs.

Day 10-11: Lake Titicacca tour
QUESTION: Any companies or guides that would do a small group tour that you recommend ? (6-8 pax) Would you do a home stay? What are the NOT TO MISS sights in the islands that are less touristy and more unique?
>> Highly recommend Allways Travel. (http://www.titicacaperu.com/). They had us pay our home stay family directly, so we know they were paid fairly. Highly recommend a home stay on Amantani. It was an amazing experience. Your group might have to split between two families due to space, but you'll still be together for afternoon and evening activities. The only thing touristy we saw was Uros, the floating islands. Even though it was definitely marketed to tourists, I would still recommend seeing them. Very cool. Amantani and Taquile are not touristy at all. Your tour group will have all the activities planned. I'm not sure you could truly go around the islands on your own, but maybe someone here has info about that.

Although I do not really think you have done much research, or the answer to Q1 would be easy to find, I will answer

Star Peru, Peruvian Airlines, or LCPeru.