Hello Stitch,
Kansai Airport - Tokyo, the best way to travel this route is to directly take the Haruka Express from Kansai Airport to Tokyo. The journey takes about 80 minutes and is covered by the JR pass. (¥ 3,170 without).
Kyoto - Hakone, for this take the Shinkansen from Tokyo to Odawara station. From here you can use local trains to explore the Hakone region. The Shinkansen to Odawara is also covered by the JR Pass. (¥ 11,880 without)
Hakone (Odawara) - Osaka, Simply take the Shinkansen from Odawara station to Shin-Osaka station. For here you can use local trains to travel further into Osaka. Covered by the JR Pass (¥ 12,420) without)
Travel on local lines within Osaka and for some extend in Kyoto is also covered by the JR Pass, in addition for travel from Osaka to Kansai Airport.
6.) Given the above travel, the JR Pass will cost about the same as buying normal tickets, by adding local travel you could perhaps make small savings. However the real reason to consider using a JR Pass here is that you can use it as one ticket for all your travel. Making it very convenient to get around Japan.
7.) Trains such as the Shinkansen and Haruka Express have special places for luggage. Local trains (within cities) do not offer this.
Hope this helps!
Daniel