Is super su and twrp rom specific or phone specific or not specific at all? Whenever I follow a root guide, I see a link to super su and twrp files. Is this super su and twrp file the same file for all phones or is there a different super su for each phone? Also, if it exists for each phone, is it rom specific? Do I need a seperate super su file for cm 13 and stock rom on the same phone?
SuperSU is generic, same for all (most) devices, some specific devices or methods may require a specific version though. 

TWRP is very device specific, each build is customized for the intended device. http://twrp.me is the official site for TWRP which has a database searchable by device. 

CM13 is pre-rooted, you do not need SuperSU at all.