how much money should I reserve for the toll fees (my route will be something like Nagoya - Mt. Fuji - Kamikochi, Ogimachi, Kanazawa - Kyoto - Shikoku - Miyajima - Nagoya)?
You may want to rent a car for a day around Hakone, or find creative alternatives such as the aerial cableway/cruise on Lake Ashi, local buses etc. I wouldn't necessarily consider it proximal to Nagoya, so it really depends also on the amount of time you're looking to spend in each of these places and the side roads you're interested in pursuing.

Where are Kamikochi, Ogimachi in Gifu, by the way ? One of my most beloved spots in the entire country is aroung Kiso-Fukushima, a valley dotted with ancient post towns on the Nagano Nakesendo trail, magnificent views and beautiful scenery and a still strong historical flavor.