Are we allowed to use the DEV@cloud build tools (https://repository-cloudbees.forge.cloudbees.com/distributions/ci-addons/) in on-premises Jenkins instances (i.e. non-DEV@cloud environments)?
Are we allowed to mirror https://repository-cloudbees.forge.cloudbees.com/distributions/ci-addons/ to our own internal system that is not reachable by the internet?
Yes and yes. The DEV@cloud addons repository is public and available to anyone, so you may do with it what you will.