7 day JR Rail Pass vs indiv tickets?

Hi,

I've been researching whether it's worthwhile to purchase the 7-day JR Rail pass but I'm having difficulty because of my confusion with Hakone, so I thought it would be easier to ask.

I'm flying in on 29th Nov to Osaka, arriving at Kansai airport at night. Then I will base myself in Osaka until 2nd Dec where I'll leave for Kyoto. Staying in Kyoto until 5th when I will head to hakone. Leaving hakone after one night to Tokyo (so 8 days in total).

I was going to purchase West Kansai JR Rail pass for 2 days (4000 yen) for 1st and 2nd Dec to travel to Himeji, Miyajima and Kyoto but I heard transport from Kansai airport already costs 1500 yen. From there, going to Hakone from Kyoto costs approx 12000 yen and I have to purchase Hakone free day pass (confused whether this is covered by JR rail pass and if I really need it once I get to hakone?). From hakone to Tokyo is 2000yen. It's still less than 28300 yen for JR rail pass. That's just my research though. Apparently there are more costs associated other than what I listed above.

Questions:
1. How does West Kansai JR rail pass work? If I arrive at night, and use it to travel from airport, is that considered one day, or will it expire 24hr from time of use?
2. Should I buy JR Rail pass (7 days) and start using it the day after I arrive (so it expires after I get to Tokyo)? Or should I just buy tickets individually (as listed above)?
3. Is Hakone free day pass (3900yen from Odaiwara) worth buying? Do I need it? Is it included in JR Rail pass?
4. Are tickets from Hiroshima JR Rail station to Miyajima included in JR Rail pass 7 days?

Thanks in advance for your help.

How does West Kansai JR rail pass work? If I arrive at night, and use it to travel from airport, is that considered one day, or will it expire 24hr from time of use?

It is based on calendar days (midnight to midnight). Note also, that it is only valid as far as Himeji. It does not cover Miyajima.

Should I buy JR Rail pass (7 days)

Your only major trips are the round trip to Miyajima and the trip from Kyoto to Tokyo. These three trips alone cost more than a 7-day Japan Rail Pass. Therefore, I recommend to use a 7-day rail pass to cover these three major trips. The other trips are minor trips and relatively inexpensive. You can consider day passes for Osaka and Kyoto.

Is Hakone free day pass (3900yen from Odaiwara) worth buying?

Depends on your itinerary within Hakone. For example, if you do the classic round trip, the pass will pay off. But if you, for example, only take the bus from Odawara to Lake Ashi and back, then individual tickets will be cheaper.

Do I need it?

No. It is also possible to pay for individual tickets.

Is it included in JR Rail pass?

No.

Are tickets from Hiroshima JR Rail station to Miyajima included in JR Rail pass 7 days?

Yes, if you take the JR Sanyo Line from Hiroshima to Mityajima-guchi Station and then the JR ferry to Miyajima.