I need to integrate my software with eBay, Facebook, Twitter, etc. Where would be the best place to ask those questions (about specific API usage)?
All API questions are on topic on SO, provided they don't have other issues—they may be too localized. If, as Robert Harvey mentioned below, "the only hope for answering them is if one of the company representatives happens to stumble over the question, it is too localized."
Though bug reports should go to the API providers. Also certain kinds of support questions (these become too localized as well).