I suggest you take an express bus from Shinjuku bus station to Mishima bus station directly. It takes 2 hours and it is very frequent on weekdays. There is no need to transfer and time journey is almost like taking trains which involves few transfers. You may check the schedule from Shinjuku bus station as I understand the schedules varies from season to season. Upon arrival on Mishima bus station, there is a direct bus to Mishima Skywalk which takes less than half an hour. Good to check the weather forecast before you go as you may not able to see Mount Fuji when weather condition is not favourable. Hope the info helps.

To get this Sky walk 1) Mishima station is station of JR Tokaidou line and Shinkansen. 2) Then get Tokai bus, the bus depart from No.5 spot from the JR station. It takes 20 min from the JR station. I recommend to visit Hakone area using local bus.

You can use Tokai bus between Sky walk and Mishima Station. There are two bus / hour from 9am to 4pm. It takes about 30min and fare is 560 Yen. You can also go to Motohakone, beside Ashinoko lake, using this bus. I recommend this plan.

lol, It's hard to said. It depend of the weather in Mount Fuji. Some times you can see from fall away, but must of the time not.

Only one condition is required, the clear sky. Rainy season around Hakone area is usually end of June to middle of July. However even rainy season, several clear day is expected. According to my experience, morning time is good to see Mt.Fuji. After 10 am, Top of Mt.Fuji has chance to covered with cloud. In that case you can see only foot hill of Mt. Fuji.

To get this Sky walk 1) Mishima station is station of JR Tokaidou line and Shinkansen. 2) Then get Tokai bus, the bus depart from No.5 spot from the JR station. It takes 20 min from the JR station. I recommend to visit Hakone area using local bus.

1,000Yen par adult, 500 yen par person High-school students and Junior high school students.