I want to start off by saying, I'm a total newb to Graphene and trying to learn and take privacy more seriously.
My questions is, if I download a google app like gboard from Aurora or fdroid and remove all permissions and connectivity, can I be confident that it is not still leaking my data? Also, if I have an app like gboard used across multiple profiles will it some how link those profiles?

    Welderup google app like gboard from Aurora or fdroid

    You can't get Google apps from Fdroid.

    remove all permissions and connectivity, can I be confident that it is not still leaking my data?

    Inter-process communication (IPC) exists, so you can't be completely confident. This is why a separate profile for Google/GSF-dependent apps is typically recommended.

    Also, if I have an app like gboard used across multiple profiles will it some how link those profiles?

    Profiles are isolated hence the recommendation of separate profiles. I doubt that any links could be formed across profiles.