How to transfer existing category to a new URL

I want to take (1) category from an existing site, copy it, and put it on a new site. I already set up the new site using the same theme. My questions:

1. Do I have to create the same category hierarchy BEFORE transferring files from the database? For example, if the category I want is a subcategory, do I need to create both the parent and child category before I transfer the database over, will it create the categories automatically, or are categories not important in this case?
2. Can I copy just the database files from that particular category or would it be easier to copy the whole database of my existing site and then delete what I don’t want?
3. Do I have to transfer all the WP files too? I don’t want any of the design to change. Just want to transfer ~400 posts that were published on the existing site already.
4. Are there existing directions for doing this?

THANK YOU!