Welcome to Interact.
Media Center makes no changes to how you organize your files unless you explicitly tell it to. If you do decide you do want to make changes, try the tool: Library Tools > Rename, Move, & Copy Files.
As for tagging, it should work fine to mix and match programs. Media Center has excellent tagging and makes every effort to be standards compliant. You can also optionally configure the program to automatically detect tag changes made by other programs by configuring Auto-Import to watch your media folders.