Strictly speaking it is, however "ulv" has a much older feel to it and would sound out of place in conversation.

What Reqviem just said. It's largely archaic.

I wrote 'en grå älg' and it corrected me with 'en grå ulv' so...

Almost. En grå varg and den gråa vargen respectively.

"The grey wolf" is sometimes translated as "Den grå vargen" as well.

Grå is singular and gråa is plural