Should by the JR pass?

Hi there,
Ihave planed to Japan thi April on 5th April, im in consideration whether i should buy a JR pass bc my route should be :
Tokyo-Hakone-Kyoto-Osaka ( My flight arrive in Tokyo and depart from Osaka so no need to return Tokyo). As far as i know Hakone have to buy the private ticket and cannot use JR in Kyoto. so my questions are:
1. Do i need to buy to JR pass to travel on hat itienary?
2.Is there any 2 day pass (that i can use unlimited bus and trains within Tokyo)
3.Could you please tell me information to get Hakone from Tokyo and Hakone to Kyoto? (which bus we have to take which train, which way is saving money)?
Im looking forward hearing from you because this is the 1st time i travel to Japan, and i also want to come back again so need to get more info about transportation here.
Thank you