Don't like to agree with Bill (or anyone else), but ...

1. So how can the United States advance stability in states going through political upheavals with a religious or sectarian element?

In reality it can’t. Egypt should demonstrate the limited capability the US has to influence internal affairs even where there is a functioning government in place. In specific situations there may be carrots that we can offer but these are internal matters that are difficult to influence.

2. What actions can the international community take to prevent the growth of violent religious extremism in failing or failed states?

Directly addressing violent religious extremism, I am not sure that there are any. Indirectly, the international community can agree to deal with the issue of failed states by creating an UN sanctioned organization that can enter these areas and restore stability. This organization cannot be there to support any single concept of government. It will have to be willing to bend to what the local population finds appropriate, which may or may not include religious tolerance. So while this answer may provide no assistance to the end you are seeking to achieve it may limit the damage caused by violent religious (or ethnic) extremism as well as limiting future retribution committed to avenge the original attacks.

3. How should stability operations engage religious justice systems about human rights, women’s rights and minority rights?

Probably shouldn’t. As much as we may not like it these are local issues. This doesn’t mean that we stand by an allow genocide like the UN did in Bosnia and Rwanda or to allow inter-religious conflicts to continue but whether we can stop other strictly religiously sanctioned acts of violence against members of the same religion I am less sure about.

4. How can civic space be enlarged to amply voices promoting religious tolerance?

I think your emphasis on the civic space is wrong to start with. You assume away your problem by assuming you have a civic space that accepts the idea of religious tolerance. This is a very complex issue. Each society will present its own opportunities and challenges. Not sure a single answer exists.