Kansai to Kyoto train late night transfer

We arrive in Kansai airport sat 28th oct 7. 30pm, we also need to collect our jr pass. Do you think we will have enough time to clear customs and colllect jr pass to catch the last express train to Kyoto at 10.15? Or would it be best to book a private transfer via bus? Do I also need to book for the express train haruka? Or can I do this on the night? Any ideas would be great :)

Do you think we will have enough time to clear customs and colllect jr pass to catch the last express train to Kyoto at 10.15?

Unless your flight arrives with a considerable delay, it should be no problem. And even in the unlikely case you miss the 22:15 train, there are other train connections to Kyoto (which require transfers along the way) until after 23:00.

Or would it be best to book a private transfer via bus?

I am not familiar with that option.

Do I also need to book for the express train haruka? Or can I do this on the night?

The Haruka has both reserved and non-reserved seating. Because your departure time is unknown due to many unpredictable elements (such as exact arrival time), it is not recommended to make a seat reservation until you arrive in Japan. The basics about transportation between Kansai Airport and Kyoto are explained here:
http://www.japan-guide.com/e/e2033.html?aFROM=2033_2158

How to use trains in Japan:
http://www.japan-guide.com/e/e2016.html

Thank you for your help:)