The goals of OpenID and IndieAuth are similar. Both encourage you to sign in to a website using your own domain name. However, OpenID has failed to gain wide adoption, at least in part due to the complexities of the protocol. IndieAuth is a simpler implementation of a similar goal, by leveraging other OAuth providers and behaviors that people are already accustomed to.
Yes, your rel="me" links do not need to be visible, but the html does need to be on your home page. You can hide the links with CSS, or include them as <link> tags in your html head.
Yes, the assumption is that people are willing to own their online identities in the form of a domain name. It is getting easier and easier to host content on your own domain name. See "Getting Started on the Indie Web" for some suggestions, including mapping your domain to a Tumblr blog, or signing up for a simple web hosting service like Dreamhost.
This service exists for websites to use if they don't want to implement OAuth code for each provider. As a user signing in to the site, you don't need to worry about whether the site is using indieauth.com or some other RelMeAuth service.
If an application is using IndieAuth.com as an auth service and IndieAuth.com is down, then logins to that website will not work. However this is just the same as if that site's own internal auth service is down had they implemented it themselves. Because of this potential risk, it is possible that some apps may wish to run their own instance of this software or implement RelMeAuth directly to avoid relying on a third party service.
We gladly welcome new providers! The goal is to support as many as possible so users are not reliant on any one in particular. Here is what you need to do to be supported by IndieAuth.
Google+ profiles only put the rel="me" attribute on links for personal pages, not for business/brand/place/community pages. The "Links" section on the "about" page of a Google+ profile contains several subsections including "other profiles", "contributor to", and "links".
For IndieAuth to work with Google+, the link back to your website must be in the "other profiles" subsection, which must be visible to the public, and you must also have the "Links" section visible to the public.
IndieAuth.com requests the minimum permissions from each OAuth provider. In some cases providers do not provide a scope that only verifies identity without also giving access to data such as public tweets.