For BN books:
If the books is downloaded to your device, then wifi is not required. Check to make sure that it is actually downloaded and doesn' t have the cloud symbol on the book. If the cloud symbol is there, then it isn't downloaded and you'll need wifi on to download it before you can read it.
For non-BN books: Epubs can be read on the device unless they are not drm free. If you bought a book at kobo,it may require the kobo app or to be opened with the Overdrive app. Kindle books will require the Kindle app unless you convert them to epubs using software like Calibre on your PC (this is free). You won't be able to convert kindle books that are not drm free.