Currently, homebrewing the Wii U does not expose you to a risk of being banned by Nintendo unless you cheat in online games. You should, however, always be careful with launching downloaded homebrew, especially if you don't trust the source, as homebrew can potentially damage your system!
Haxchi is a secondary entry point which uses certain DS Virtual Console titles to allow for access to homebrew while being completely offline (still works with online but no connection required to launch CFW)
Haxchi is not required, however, if you want to use homebrew on your Wii U while offline you will need it. It’s highly recommended as it’s more stable than the browser entry point, especially on the newest firmware.
Yes. It is, however, a bit more complicated than installing from SD Card. Detailed instructions are in the `Install from USB` tab in the [Dumping guide](dump-games).
No, you must have an SD Card for a first time setup. A USB can then be used to install game backups, Virtual Console injects, etc, but not to store homebrew applications which are required to set everything up.
Nothing special, you can leave them there, delete them or replace them with new ones. Those files are not used in the process, and therefore, won't have any impact by being or not being there.