im playing as the chislev right now and im about 500 or so turns into it and ive researched writing which should give me the option to build the great library. it shows up gray in all of my cities though. that and that guild that is required to train the wandering mage also is researched but it wont let me build that either in any of my cities. what are the required buildings for these?

not sure about the silver circle, but the great library requires that you have built 3 libraries in your cities ( although the exact number of libraries probably changes with map size)

No it doesn't. It's plain fixed 3.

that guild that is required to train the wandering mage also is researched but it wont let me build that either in any of my cities. what are the required buildings for these?

The Silver Circle headquarters requires both Currency and Alteration - though it may be visible (greyed out) with just one of the two researched. Other than that, it just requires that there's no other city on your team (including permanent allies) who is currently building it.