Fuji Hakone Pass

Hi guys! So on 31 May, I will arrive at Kawaguchiko from narita airport. And 1 June I will start travelling around. So my itinerary is: 1 and 2 June full day in Kawaguchiko, 3 June going to Hakone through gotemba premium outlet, 4 june full day in Hakone, 5 June going to Shinjuku from hakone. So I need some advice from my fellow travellers:

1) I was thinking to buy Mt.Fuji 2 days pass (8000 yen) for 1-2 june and Fuji Hakone 3 days pass (9090 yen, round trip to Shinjuku) for 3-5 june, so it can cover the cost from kawaguchiko to gotemba and hakone, and also my trip to Shinjuku. However, is it possible to buy the fuji hakone pass (the one that cover trip to shinjuku as well) at kawaguchiko station? And is it already the best option for the cost?

2) I will bring luggage to the gotemba premium outlet, and as I know they provide an extra large locker there. But still, is it a good idea to go there with a luggage? I chose this option because I thought if I put my luggage in my airbnb in hakone first, then i will waste a lot of time since to go to Hakone I have to pass gotemba as well..

3) If in fact I cannot buy that fuji hakone pass in kawaguchiko, is there any advice for how much will be the transport from kawaguchiko to Hakone? And is it worth it for me to buy the fuji hakone trip at hakone after that? (Assuming I already paid separate cost for the journey to hakone, and I will use fuji hakone pass for going around there and my trip to shinjuku).

any help and advice is very much appreciated! Please help this fellow traveler who will have her first adventure in Japan!! :D
n.b I will travel with other 9 people (6 old people, 4 young people)