Transportation in Japan

Hi, we have 4 of us will be travelling to Japan for the first time from 10-16 December 2015. Can anyone advice us on how to travel economically in Japan. We've no idea how the transportation work in Japan.

Our schedule as below:-

7/12/2015 - Arrival to Narita Airport @ 6.30pm, then check-in to Grids Hostel Lounge Akihabara (near to Asakusabashi Station)
Question: Is there any direct train from Narita Airport to Asakusabashi Station? And how much is the fare?

8/12/2015 - Transfer from Akihabara to Kyoto
Question: Shall we buy the PASMO/SUICA card in airport so that we can travel from Asakusabashi Station to Tokyo Station for Shinkansen to Kyoto?

9/12/2015 - Kyoto to Nara to Osaka to Kyoto
Question: Will it be economical for us to buy the 7 days JR pass nationwide or the JR west rail pass 2-days?

10/12/2015 - Kyoto to Mt. Fuji (Fujisan Station)
Question: How to travel from Kyoto to Fujisan Station? Shinkansen to Fuji station, then any train/ bus to Fujisan?

11/12/2015 - Mt. Fuji to Shinjuku Station
Question: Which way will be cheaper to travel back to Tokyo Shinjuku if we are holding the JR pass? Train or bus?

12 /12/2105 - City tour in Tokyo
Question: Which option is better to purchase the PASMO/SUICA card or Seishun 18 Kippu for Tokyo city tour?

13/12/2015 - Tokyo to Enoshima & Kamkura to Tokyo
Question: Can we use the JR pass that we purchase earlier to travel to Enoshima & Kamakura?

14/12/2015 - Disney Land Tokyo
Question: Can PASMO/SUICA card use to travel to Disney Land?

15/12/2015 - Shinjuku to Narita (Richmond Hotel Narita)
Question: Can PASMO/SUICA card use to travel to Narita City?

16/12/2015 - Narita City to Airport (by hotel free shuttle bus)

Thanks alot in advance for all your advice :)

9/12/2015 - Kyoto to Nara to Osaka to Kyoto

You're packing Kyoto, Nara, AND Osaka in one day?!? What's the point? You're not going to see much in any city at all if you're only spending a few hours in each. Pick one, or add more days to this part of the trip. But honestly I think visiting this area for just one day is a waste of time. If you're that short on time, stick to the Kanto/Tokyo area. You've already got a lot you're doing.

As to your train questions, if this is your final set itinerary, I would get the 7 day Japan Rail Pass. Activate it on the 7th. It will cover your round-trip to and from Kansai plus your last day of it going to Enoshima/Kyoto. You'll pay regular train fares for the last 2 days, or you can get a Suica card and load it up for ease of travel.

There is no need for you to buy the Seishun 18 kippu. If you decide to scrap Kyoto and just stick to the Kanto area, you should not buy a JRP either. Instead, just get the NEX/Suica package.

Suica is not a discount or package card by itself, it just streamlines travel. It can be used on all JR trains and these days most of the Metro lines and even a few of the private lines use Suica. I think you would benefit from reading through the pages linked here: http://www.japan-guide.com/e/e627.html It will explain lots of the basics.

For train schedules and "how do I get from X to Y" questions, use http://www.hyperdia.com

Well if it is just two cities it is possible.
E.g. Viewing Nara in the day and domtombori at night
E.g. Doing Fushimi Inari, Kiyomizudera, Kinkakkuji, Arashiyama in the day and Domtombori at night

Though, I would only recommend this if the traveler has no intention to ever return to Japan.

Thank you for your advice. :D

For me - to do Nara quickly is a long half day (including transport). To do Kyoto any justice is a full single day. All together - I've spent around 2 weeks in Kyoto and probably visited around half of the major sites (and I travel fast compared to most people!) I've not visited Osaka (apart for work) so cannot make any comment.

Kamakura is nice - but I think it's more important to spend an extra night in Kyoto/Nara than visit Kamakura.