I split off answers about branding into a new topic: WriteFreely Branding – feel free to continue that discussion there!
That’s correct, the /api/ path will always be there, so you can simply ask for the host (e.g. writefreelyinstallation.site).
No need to add sign-up links unless you think it’d make the experience better for users. In that case, we’d recommend simply sending people to Write.as or the WriteFreely instances page, where they can find a community to join.