For instance, if a study was conducted studying the impacts of climate change on various systems of a developed country X and I repeat the research with data set of a different country Y, or will it be considered unethical and plagiarism?
It is not unethical. However, the study should address the peculiar challenges (local context) of the study area for it to be scholarly to merit academic recognition.
There is a lot of value to cross-cultural research, so you should definitely consider doing what you propose.
In general, plagiarism involves much more direct borrowing from another researcher. You could think of it as taking someone's words or ideas without giving them credit. Instead, when you build on previous work, you use careful references and citations to show how it haas guided your own work.
I don't think that's a problem, because what matters is the originality of the research. This originality can be in the results obtained as well as in the approach and the method with which the problem has been treated.
Absolutely. This type of study helps further the previous work, enhancing it by referencing them and demonstrating how the same model is applicable or not in other conditions.
As others have indicated, you can definitely make a substantive intellectual contribution to the relevant knowledge base by conducting research in a new context. Make sure you attend to the peculiarities of that context, and the implications for other settings with similar circumstances if relevant, but otherwise don't worry about plagiarism -- you're forging new knowledge!
In my opinion, there is no problem in doing such work, because your context/situation is different from the study already conducted, means you have your own research gap there with reference to your locality. doing such work will also not called as plagiarized, because the concept of plagiarism is different.