12days in japan

hi there.. my interary is osaka ( 1days ) kyoto 3days cover nara 1day trip then go to takayama (2 or 1day) then to tokyo.. in tokyo would like go to hakone 1day trip, mount fuji, go to azumayama park, kawachi fuji and hitachi seaside park..

1. how much transportation fare if i use normal train? should i buy JR PASS 7days?

2. im coming early april..is it worth i visit hitachi park? where u suggset if i want to visit beautiful garden in japan? i really love flowers!

3. and dis is the most hard for me to research.. i would like to go to any cat island.. where u suggest that nearest place that i mention in my internary.. even the okunoshima island.. but i dont understand the direction.. can u help me? thank u! :)