Hi there,
Regarding your question 1), there is a direct bus from Shibuya to Kawaguchiko. You can book seats from the following website.
http://highway-buses.jp/fuji/
If you scroll down the page, you can find the link for (From Shibuya to Kawaguchiko/Mt. Fuji/FujiQ Highland). Please make a reservation from there.
There is also a ticket office in Shibuya station, so pleaes pick up your ticket at the counter.
Please see the link below for the access to the office.
https://www.highwaybus.com/html/gp/foreign/shibuya/en/index.html
Regarding your question 2), there are no direct bus from Kawaguchiko to Narita Airport.
It all depends of the time, however, if you can take a Narita Express leaving at 2:14p.m. from Kawaguchiko,
that will be the fastest way to go to Narita Airport.
Please see the link below for your information. (Sorry…Japanese only)
http://www.fujikyu-railway.jp/train/jr_train01_2015sp.php
Otherwise, you can go to Shinjuku Sta. by a highway bus (http://highway-buses.jp/fuji/) and take a limousine bus to Narita Airport. The other way is taking a Yamanote line from Shinjuku Sta. to Nippori Sta. and take a Keisei Skyliner to the airport.
Please be noted that it will take a quite long time to go to the departure gate after getting off the train.
If I were you, I will use a Narita Express or take a limousine from Shinjuku station.
It is easy to find the limousine terminal in Shinjuku since it is near the Keio Highway Bus terminal.
I hope this help you make the best decision for your transportation.