Yes that is definitely true, my only hesitation is that the pass is only for ordinary seats, not green car. But it definitely would save money so might get it anyway.

Note - The Kansai Hiroshima pass is not valid on the Tokaido Shinkansen from Kyoto to Shin-Osaka. It only covers you for the Sanyo Shinkansen (operated by JR West) from Shin Osaka to Hiroshima. If you're staying in Kyoto, you would need to take a non-Shinkansen train as far as Shin-Osaka (or pay the Shinkansen fare for the section between Kyoto and Osaka).

I was wondering if it is worth visiting USJ in July? I know it will be hot and exceptionally crowded - though I can buy an express pass even though it's expensive. Or just wait until I'm back in July at another time of year like spring or winter.

Hard for anyone to answer for you. Hot and sticky July in any year is a suboptimal time to be shlepping around an amusement park and waiting for rides. It might be especially crowded this year with the added influx of expo tourists. But perhaps it's really important for you to go to USJ, and perhaps you're not sure when you'll get the chance again. If that's the case, I think you need to take whatever steps you can to mitigate the pain.

On the other hand, if you know that you'll be back next spring, preferably before the school holidays ...