Train fare rules regarding child are:

Child 5 years old or younger ride free if accompanied by a person 12 years old or older, if a child does not occupy a seat by themselves. If 5 years old or younger will occupy the seat by themselves then the child need to pay the fare.

One person can accompany up to two 5 years old or younger for free. For example, one 30 years old accompanying three kids 5 years or younger. Third kid has to pay the fare.

If 5 years old or younger ride a train my themselves then fare need to be paid.

As for your question about Kansai Thru Pass, not exactly sure about getting to the places faster. Kansai Thru Pass will give you unlimited ride on non-JR trains. Are you indicating that you will get to places faster on JR trains?

It is all dependent from where to where you are planning to visit. JR Kyoto station is located at south portion of the city. Kawaramachi and Sanjyo of Kyoto which is served by Hankyu Line and Keihan Line (you can use Kansai Thru Pass) is more of central location of Kyoto. Hankyu Line and Raden Line (can use Kansai Thru Line) take you to Arashiyama, where JR cannot.

From Kyoto to Nara, JR and Kintetsu Line (can use Kansai Thru Pass on Kintetsu) both are pretty much same time of journey, If you looking at faster, then fasted between Kyoto and Nara is Express train of Kintetsu Line where reserved seating where you have to pay surcharge.

If you are thinking Shinkansen is faster, again, JR Kyoto station is at south part of the city and Shinkansen will take you to Shin-Osaka which you will likely require few extra transfer to get to place you want. Not sure how much saving you will get in time wise.

If you can provide specific to/from location then we can compare the actual journey time.