http://canonizer.com/ already has most of the features you just described.

• Propositions are made by users, and are editable by users. Not exactly like a wiki, but with a voting mechanism for proposed changes to existing propositions.
• the propositions are templated, but currently don't include a picture. They include an "Agreement Statement", a list of supporters, and a tree of subcamps.
• there is a crude mechanism for indicating your degree of acceptance in each proposition. You don't specify an exact number for your support, instead you list the propositions in order of most supported to least supported, and numbers are automatically chosen based on this ordering. and you can choose to support other users, not just specific propositions.
• yes, there is a tiered structure to the proposition networks. A tree structure, actually.
• yes, there is a mechanism to form groups. These are called "camps"

• there are some experimental methods to promote individuals, but currently these don't really work well.

• 1.there is already a node for "other people experience qualia, just like me", but I haven't found any existing node yet for "other people are real, just like me". And yes, you can set your contact details to be private

• 2.yes, you can comment on, edit, or fork any existing proposition, even if you're not a supporter of that proposition. But the other supporters have to approve your change before it becomes official.
• 3."What is God?" is the most active node on the site.
• 4.There is currently no special "moderator" role. Any user can submit a proposal for a change to a proposition, but all current supporters of the proposition must agree to the change before it becomes official. But there is a "Mind Expert" role, which is basically a user whose opinions count for more points than regular users, in the fields that they're an expert on.
• 5.yes, you can use canonizer to do stuff like this. You can also set up a private canonizer account on your own website.
• 6.Currently there's only one person working on this project, and he hasn't set up hosting for the source code anywhere yet. Contact Brent Allsop if you want to help with the coding. If you just want to take a look at the current source code, you can download it from these two zip files.