Your questions are about the access to a version control system, rather than the code.
As I've already said, code becomes Open Source when an Open Source license is embedded in the code text. It retains that license as it travels. This idea, and its leverage of copyright laws predates and is independent of code versioning.
To paraphrase a little: your question is like asking whether a haiku, as a type of poem should have a different name depending on when it is written in pen or pencil. Which is that you are mistaking the tool for the content.
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Your questions are about the access to a version control system, rather than the code.
As I've already said, code becomes Open Source when an Open Source license is embedded in the code text. It retains that license as it travels. This idea, and its leverage of copyright laws predates and is independent of code versioning.
To paraphrase a little: your question is like asking whether a haiku, as a type of poem should have a different name depending on when it is written in pen or pencil. Which is that you are mistaking the tool for the content.