It appears that you'll be in Japan for 10 nights? If so, presumably you'll get a 7 day JR Pass .... in which case you need to activate it so that it covers days 4 -10 (or it'll expire before you get back to Tokyo) so no need to exchange it at Haneda - do it at Shinjuku (or Tokyo) station.. Get a Suica card when you arrive at Haneda and use that for the monorail into Tokyo and the subway/trains/buses in Tokyo and Kyoto (except once the Pass is active and you're taking a JR train).

As has already been suggested, take the train from Kyoto to Narita. It takes about 4 hours so if you leave Kyoto late morning/lunchtime, you'll be at Narita in time for a 6 pm flight. If you can, change to the Narita Express (NEX) at Shinagawa rather than Tokyo (just easier, particularly if this is your first time in Japan),

As for cash, use a debit card at a 7-11 ATM. Most foreign cards don't work in Japanese ATMs, 7-11 and the Post Office being the notable exceptions. 7-11s are everywhere (there'll be one at Haneda somewhere) and many are open 24 hours. Obviously a card that doesn't charge foreign transaction fees is preferable. The 7-11 ATM may charge you a fee (yes if you're using a Visa card, probably no if it's a Mastercard) - either ¥108 or ¥216 depending on the amount you withdraw. It will tell you that up front and it will be separately disclosed on the ATM receipt.

In addition to the subway/bus/trains, you can use the Suica card at convenience stores (7-11, Family Mart, Lawson) - and Japanese convenience stores ('konbini') are excellent. You can also use the Suica card at some cafes and vending machines (which are everywhere in Japan -- believe me, you've never seen so many vending machines).

Why do you want to go to Toyama? In that part of Japan, most people would go to Kanazawa. As for luggage, if you're only there for 10 days, presumably you won't have much luggage .....