Answer 1: Swagger is the de facto. It seems to have low actual usage, but high midshare. As time goes on, I expect there to be a much higher usage of Swagger, since pretty much all API services accept it.
(Other options include RAML, Blueprint and IO Docs, but Swagger has the momentum)
Do you know any projects that reverse this functionality (generating API documentation from code)? I know that https://github.com/timothycrosley/hug intends to provide this in the future, but could not find one for other languages (Javascript would be useful right now).
Yeah, it's not. It's still what people in big enterprises do, or what people who want to do a quick API use.
If you're a .NET developer it's pretty easy to consume WDSL/SOAP services, so you might be more inclined to just use it when creating your own webservices.
There's of cause also the group that doesn't really know what they're doing, who just slaps a webservice method decorator on whatever internal function they wish to expose. Those are usually the worst APIs.
Another cool thing (potentially) about swagger is that AWS is supporting it for their API Gateway. You scan write a spec in swagger, tie it to AWS Lambda "functions", and AWS will create/update that . Still a WIP though :(
You may want to take a look at Swagger-Codegen (https://github.com/swagger-api/swagger-codegen) as well to generate ASP.NET 5 server stub or C# API client given a Swagger/OpenAPI spec.
Disclosure: I'm a top contributor to swagger-codegen
(Other options include RAML, Blueprint and IO Docs, but Swagger has the momentum)