Yes. In Swedish, the singular form for moose is "älg," and the plural form is "älgar."

Yep, like fish and sheep

Yes, the original Cree plural ('moosoutch') isn't used anymore, but when talking about the European elk ('älg'), the plural form 'elks' may still be used when referring to a specific group / selection rather than all elk there are. Not sure if the same works for 'mooses' though.

But "mooses" seems to be accepted

Giant cupped palmate antlers (Alces alces): "Moose" in America, "elk" in Europe. Limited European populations in Baltic states and Scandinavia.

Giant, branchlike velvety antlers (Cervus canadesis): "Elk" in America, "wapati" in Europe. Native to remote eastern Asia and northern North America, no populations in Europe.

If you say "älg" to a Swede, they'll be thinking of a Bullwinkle, not the deer-looking things.