tokyo-koyasan-nara

I will travel from Tokyo to Koyasan using the JR Pass until Osaka and then getting a ticket/pass (?) to Koyasan. Is the Koya line from Namba a direct line? Should I book the ticket in Tokyo due to the busy period? From Koyasan I will go to Nara: should I go back to Osaka and then get a train from there or there is a different and faster alternative? All your help will be very appreciated :)

Is the Koya line from Namba a direct line?

Limited express trains travel directly to Gokurakubashi Station, where you transfer to the cable car. By express trains, a transfer at Hashimoto Station is usually required.

Limited express trains are faster and require a surcharge and seat reservation, while seat reservations are not possible on express trains.

Should I book the ticket in Tokyo due to the busy period?

I have the feeling that except on very busy days, the limited express trains between Namba and Koyasan don't get booked out. And even if they do, then you can still ride an express train. I personally would not make reservation for the Nankai trains until arriving at Namba (or Shin-Imamiya Station, which is the better transfer station for Japan Rail Pass holders than Namba).

As for reservations for the shinkansen, I recommend to make them in advance, if possible.

From Koyasan I will go to Nara: should I go back to Osaka and then get a train from there or there is a different and faster alternative?

The faster way is via Osaka. But you can also take Nankai Railways only as far as Hashimoto Station and transfer to the JR Wakayama Line there to Nara. It takes more time, but is cheaper for Japan Rail Pass holders, and the scenery is quite nice.

I am just checking the timetable on www.nankaikoya.jp/en/iku/01.html
and it seems that around 11am there are no trains from Namba on a thursday... Does it include the day of the candle festival (13th Aug)?
is that timetable actually updated?
Is the hyperdia link only for JR trains (i cannot work it out)?
second question: On our way back from hiroshima to tokyo, we would like to stop to Himeji. Do you think is worth it or you can suggest another option for a few hours stop on the way back?
thank you very much XXX

and it seems that around 11am there are no trains from Namba on a thursday... Does it include the day of the candle festival (13th Aug)?

No, there are additional trains during the festival.

On August 13, the following additional trains will be running from Namba:
Koya 5, departs Namba at 11:00
Rinkan 3, departs Namba at 12:34

Furthermore, there will be additional trains between Hashimoto and Gokurakubashi.

Information in Japanese:
http://www.nankai.co.jp/traffic/info/summer/index.html

Is the hyperdia link only for JR trains (i cannot work it out)?

No, it includes Nankai trains, but I am not sure whether it correctly displays the temporary trains during the festival.

On our way back from hiroshima to tokyo, we would like to stop to Himeji. Do you think is worth it or you can suggest another option for a few hours stop on the way back?

If you are interested in castles, it is certainly worth it. Even if you have just a slight interest, it is worth it, because it is Japan's most beautiful castle.