I am looking for an app for my iPhone and iPad, equivalent to Font Book on the iMac. I would like to be able to download a variation of fonts to use in Pages. Does this exist?

there very well may be such apps

but this sub forum is for Accessories like headsets and cases and the likes so

people who knows more about Pages and fonts will not be likely to come by and read it

If I were you I would most likely post my question in this subforum made just for iwork for ios

https://discussions.apple.com/community/app_store/iwork_for_ios