tokyo-koyasan-kyoto

I recently looked at the main JR pass website and hyperdia and both had these warnings that some trains might not be covered by the JR pass... so just checking, these trips are all covered by the pass right? We're going first week of April :)

1) from tokyo to the shin-osaka station (closest to koyasan, from there we take other trains to the city itself)
2) from shin-osaka station to kyoto
3) from kyoto back to tokyo

Thanks a bunch for your help!