What Pass to purchased?

I will be coming from Narita in the 3rd week of December and would stay in the Akihabara area in Tokyo for approximately 8 days. I then plan to take a night Willer Bus to Osaka for the final 7 days of my trip and then departs through Kansai.
In Tokyo, I plan to visit Odaiba, Shibuya, the Disneysea, Harajuku Area, Ginza, Ueno and spend 2 days in Hakone for the purpose of picture taking with Mt Fuji in the background. I would be buying Hakone Free Pass.
In Osaka, I plan to buy a 2-day Hankyu Pass to cover my Kobe and Kyoto Trip. I would also like to visit Shirakawago for half a day.
With the above itinerary, which pass do I buy? Is purchasing a Sheishun 18 Ticket correct? Can someone please advise?

Seishun 18 Tickets is good for people who do long-distance trip on JR trains but have time for a very slow travel... and I don't see anywhere in your itinerary where that would make sense.
For you, probably getting a prepaid card (either PASMO or SUICA) and top up as you go, for travel around Tokyo area. There is no discount, but it comes in handy.

Um, Shirakawago from Osaka for half a day sounds a bit ambitious. Please check the map/access information.

To go to Shirakawago it's probably best to do it from Tokyo on the way to Osaka. Take the shinkansen to Kanazawa, and the bus to Shirakawago. Spend the night in Kanazawa, then travel to Osaka from there.

Why is Tokyo Metro not recommended?

Who mentioned 'Tokyo metro not recommended'?
Tokyo metro is good for travel within tokyo and only that. As per many other cities around the world...

I don't get it.

guest wrote "For you, probably getting a prepaid card (either PASMO or SUICA) and top up as you go, for travel around Tokyo area"
These cards are used to travel on Tokyo Metro and other transit modes..
You can use Suica in other area than Tokyo ..