The issue you are facing is that if you say:
◯◯ と ◯◯ が好きです
The list formed with と is usually assumed to be an exhaustive list of items, so if you were using it to say you liked ONLY Japanese culture and Japanese history, then it would be appropriate.
The form you showed in your first sentence:
Is awkward to the listener.
While it gets the point across, it is not something you will hear anyone say because you are trying to make the listing of "various other stuff" part of a closed list of stuff.
On the contrary the format:
◯◯ や ◯◯ が好きです
Allows the listener to infer that, while you only mention Japanese culture and history, you are not implying that is the only thing you may be liking. When listing multiple things you like, や is a superior choice.
In the Japanese language, you do not need to add something to the effect of "and stuff" because by using the correct particles, you identify that your list is non exhaustive.
This sentence is a way of saying "I like things like Japanese culture and Japanese History"
The reason this is accurate is because it is clear from your question in English, that you do not intend to limit yourself to only liking the two things you specifically mentioned.
By using や and など together, you say that your list is non exhaustive, and the など on the end sort of sticks on the list and says "and things like this" about the other things you listed.
Hope that helps.