Both cuda and cudnn are shipped with the binary. No need for you to worry about that. But the current binaries ship with cudnn 8.0.4 (the only thing that was available when they were built).
Yes that is the only option to get these two versions
The 1.7.1 binaries will ship with cuda 11.0 (EDIT: see @ptrblck comment below, this might change)  because conda still does not support 11.1   But it will have cudnn 8.0.5 which should fix most perf regressions!