Questions on train timings and frequency

How long does it take
a. by JR train
b. by normal trains (using Kansai Thru Pass) for the following routes

1) KIX -- Kyoto
2) Kyoto -- Nara
3) Kyoto -- Osaka
4) Kyoto -- Koyasan

What about the frequency of trains? Do JR trains have a higher frequency than the trains covered by the Kansai Thru Pass?

1) KIX -- Kyoto: JR limited express Haruka runs every 30 minutes. The JR West Kansai Pass for 2,000 yen would be optimal. The duration is 78 minutes.

2) Kyoto -- Nara: 38 minutes on Kintetsu express train. The express runs 4 times an hour, but in most cases you need to transfer en route. Individual tickets will do, though the Thru Pass is applicable.
JR is less frequent.

3) Kyoto -- Osaka: JR; 28 minutes on the special rapid. It runs every 15 minutes and costs 540 yen each way.
Hankyu: 44 minutes on the limited express. It runs every 10 minutes and costs 390 yen each way. Thru Pass applicable.

4) Kyoto -- Koyasan: Kyoto Kawaramachi--(Hankyu)--Umeda--(Subway Midosuji Line)--Namba--(Nankai and cable)--Koyasan
It takes 3 hours in total. Thru pass would be recommended for this trip.

http://www.jorudan.co.jp/english/

Try this website .It gives times prices etc for JR Trains-

http://www.japanrail.com/JR_hyperdia.html