Fun read, but alas factually inaccurate. Article says: "almost all European languages belong to one family – Indo-European – and of all of them, English is the only one that doesn’t assign genders that way."
1. There're quite a few languages in Europe that do not belong to Indo-European: Basque, Estonian, Finnish, Georgian, Hungarian, Turkish...
2. It is not true that English is the only Indo-European language the nouns of which don't have gender. Armenian for instance, does not and there are probably others.
You can think of "resource" as an object in your application exposed on the web. REST actually talks about "resource representations" not: resources per se. This has to do with the Facade pattern and not tying your public interface with your internal implementation.
That said, for getting started you can think as "resource" being a web-addressable representation of an object in your application.
Architectural style for building scalable applications. Fielding wasn't talking about APIs specifically.
There's nothing "weird" about links in APIs. For an easy metaphor, think of "links" in APIs as you think of foreign keys in your database tables. Link doesn't just mean something you can click :)
Unfortunately, in popular programming it has become to mean anything and everything that uses resource-oriented URLs and at least loosely: HTTP methods as verbs to "operate" on those resources.