Will be arriving at Kansai around 19:30. Would it be necessary to reserve seats on the Haruka Express to Kyoto at that time? What are the off-peak times ? Would it be possible to get to the Karasuma-Oike Subway Station from the Kyoto Station on the same ticket? Would a one day pass work better ?

Thanks in advance

I doubt you will "need" a reserved seat as there are plenty of trains and plenty of unreserved seats as well. JR operates the Hauruka express and the Kyoto subway is a different ticket so I think you'd need to buy a separate ticket (though I am not positive). You can buy a subway card when you get there.

See this site for the detail you seek. Press the to/from Kansai button on top

http://www.japan-guide.com/e/e2363.html.

You cannot use your rail ticket to ride on the Kyoto subway.See the page I left above for info on what modes of public transport are available within Kyoto. If you arrive on a train at Kyoto station simply walk over to the subway station and buy a ticket to Karasuma-Oike. Or walk upstairs and take a taxi from the stand in front of the station.

Aloha!

Thanks a ton!

Just checked the japan-guide site and if a reserved seat is not necessary then we could buy the JR West Rail Pass-Kansai Area one day pass for Y 2000. Can this pass be used on the subway?

No, as Kyoto subway isn't run by JR West but by the City of Kyoto. You'll save just under 1,000 yen by getting the Kansai Area Pass (allows you to ride in an unreserved section of Haruka Express). But think carefully if you need the pass on other days too, as it's handy for getting to and from Himeji from Kyoto (on rapid trains). You are only allowed to buy one pass per stay (though you can also buy one before arriving in Japan).