JR Pass to Hakone

Is the Trainline to Hakone from Tokyo a private line? can the JR Pass be used?

With JR trains you can only get as far as Odawara, from where you will have to use non-JR trains or buses (Odakyu) into the Hakone area.

http://www.japan-guide.com/e/e5206.html

Hopefully that's not your only destination with the JR Pass.

No, I am going to be in Tokyo first, then plan to go to Kyoto and Osaka as well, so looking to go to a number of places.

I plan to do a day trip to Odawara and Hakone.

Is there a day pass for Hakone's train and bus network? if so how much is it?

With the JR Pass you can get as far as Odawara Station.
From there though you can purchase the Hakone Free Pass which I highly recommend for the Hakone Round Course.

http://www.japan-guide.com/e/e2358_008.html

http://www.japan-guide.com/e/e5210.html

This is how I did Hakone and I highly recommend this is how you do it as well.

Isn't the Hakone pass for 2 days?
Doesn't seem to be worth it if I am only there for half or 1 day.

Is there not a general 1 day pass for the Trains?

Read the assessment for the Hakone Free Pass. If you choose to do the Hakone Round Course (which I recommend to experience everything that Hakone has to offer) the pass will pay off even if you use it for just 1 day.

''If you do the classic round course by train, cablecar, ropeway, boat and bus, regular tickets would total about 6300 yen, i.e. you can save considerably by purchasing the free pass. Furthermore, using a single pass is a major convenience over buying single tickets each time you ride a train or bus.''

http://www.japan-guide.com/e/e2358_008.html