Most algo trading is going to use Bloomberg or Reuters data, since they are very "clean" datasources that tend to be more focused on finance sectors, and not a ton of hollywood gossip. Generally they are tagged with the actual stocks in the articles, so you would have to be doing it on purpose.
Sorry, I mean an algorithm based, for example, on the number of clicks on Berkshire Hathaway articles on a financial site being influenced by Anne H. fans clicking on the wrong search result.
Most, yes, but since everyone is doing this, to stay ahead, you have to do something else if you want to do better than them. Hence mining the "regular" internet instead.