No, it doesn't do any of that. However, it does not "copy code" except in marginal use cases, the far more common scenario is that it will suggest you very basic code that is akin to a Stack Overflow reply.
I read a lot of open source code and might subconsciously absorb techniques and patterns that are common. When I write code I might be influenced by what I read, not line per line, but rather generally.
Is it like that?
Kinda, but I think you are imagining something bigger than it is. At least in my experience, it works well for simple stuff like "iterate over x and extract y" or similar queries that I imagine are well represented in its training data. When you get to very specific functions, its answer will be less reliable and more likely to be a wonky rehash of the few examples it has for that case.