I think the user's expectations are important here.
I would not suggest an system where they can donate, become instantly visible in the group, and then have to manually opt-out of the group.
Instead I think it should be a one-time, per-group configuration by the administrator.
In other words, the admin can configure "people with pledge X are automatically added to group A". "people with pledge B are ignored", etc.
Please note that you should discriminate by pledge type, not pledge ammount, as people can manually change their ammounts.
Basically user should be able to know up-front what they can expect in terms of perks / anonimity.
Your call. I think the adoption of this plugin will be higher if it has some out of the box promotion (a default promotion to make the patreon functionality visible, with as little configuration as possible).
What are the options for styling? You can only do so much with CSS. A group page is still just a group page and does not have the context of donations.
I figured that people who are looking at that list are potential patrons, so I should give them some context and make it easy for them to participate.