It is a naming confusion (see http://en.wikipedia.org/wiki/Elk#Naming_and_etymology). Russian word "лось" refers to what North Americans call "moose" and in British call "elk" (Alces alces species). The animals of species "Cervus Canadensis", which in North America is called "elk" is called "Вапити" in Russian (i.e. "wapiti"). Russians never use "Американский лось" to name an animal, because it is the same species in North America and Eurasia.

There's no real differentiation between moose and elk in Russian, since elk is the only one of the two indigenous to Russia and moose is a North American thing, so there's no real need to "split hairs" so to speak if you're talking to someone who grew up in the Russian language. They'll assume you're talking about elk.

You could theoretically call both лось and have it sound ok to a Russian speaker. It's not something you'd pick up from the language as much as from knowing Russian culture/flora/fauna.

I don't know Russian, but if this is any similar to Polish, then Лосиный will be an adjective form of the noun лось. американский just means "American".

Лось is either. "Aмериканский лось" is something that you may hear on Animal Planet in a show about elks and moose.

"American Elk Island" probably wouldn't fly too well as a place name, in any case.