When I try to update Elementor Pro, I receive this message: "Update Failed: Could not copy file..." or any other error message, how can I solve the issue?

This occurs generally when you work with Elementor Pro from a localhost. 

In this case, you can download Elementor Pro via your Elementor Account in https://elementor.com.

You will find the file in Purchases > View Details and Downloads.
Once the file downloaded, go to your WP Dashboard, delete Elementor Pro, then in Plugins, click on "Add New" and upload the file of the new version downloaded from elementor.com.