Another organization they support is Exodus International. It is published that numerous members of Exodus International attended a conference in Uganda in support of their 'Kill the Gays' bill. They have supported a number of other anti-gay organizations as well.
While Chick-Fil-A did not come out and say they are against homosexuality, it is evident by their actions. If they are not "anti-gay", then they evidently didn't research the organizations that they have donated hundreds of thousands of dollars to.
This also answers your third and fourth question.