Mirroring GitHub to GitLab

Is it possible to mirror our GitHub repositories to our GitLab that is on a local server?
Will GitLab also be updated when we push from our GitHub repository?

TIA

Yes, you can follow our Repository mirroring guide to set this up.

Pulling from any Git remote URL will work if your GitLab application’s network configuration can resolve the remote’s addresses and make a proper connection, and your passed credentials authenticate successfully.

The updates will be pulled automatically, but only at the frequency documented in the link above.

Do I need to make both repositories from GitHub and GitLab into public? Also, should the account/email address of GitHub be in public too?