hi San,
Regarding the 100 minutes All-You-Can-Eat Genghis Khan buffet at the Genghis Khan Hall, its only lamb and vegetables. I didn't eat the other buffet that includes crab.
Glad to know that you are going to stay in dai-ichi takimotokan. I would say its a good choice because they have the greatest number of different types of bath there and their service is very good.
For the onsen, you have to be naked. You can wear the yukata that is in your room's wardrobe or your normal clothes to the onsen. Take off your clothes and place in the basket or locker at the changing area. Then go to the shower area to wash your hair and body with the shampoo and shower cream provided there. If you have long hair, please tie them up.
Before you enter the onsen, splash some of the onsen water on your body to test the temperature before going into the water. One of the bath, the "Demon Bath" can be too hot for many people. If it is your 1st time going to onsen, don't stay in the water for too long. Maybe get out of the water after soaking for 5 - 10 minutes, take a rest first before going into the water again. There are a few outdoor onsens there and I am sure you will enjoy them.
Like you, initially I felt embarassed at the thought of being naked in front of others. However, once you enter the changing area and everyone takes off their clothes like nothing and naturally, you will also feel at ease to be naked like everyone else.
Are you staying japanese-style room? This is what I had for in-room dining and they are delicious. They will lay the futon for you after dinner.
Regarding Sapporo, is there any particular place(s) you want to visit? I would suggest that you plan the places carefully so that you can buy their day subway pass (800 yen) to save some money on transportation. I spend 2 days in Sapporo and wished I had stayed longer.
On Otaru, I spend a full day there. Personally feel that half day at Otaru is too short as I like to walk and see things at a slower pace. You can take some photos of the canal before sunset, then have dinner nearby before going back to the canal for night shots.