Yes. And in addition to that, the vowel should be pronounced short, not long as in the audio. If I got this in an audio exercise, I would have no idea what it was supposed to mean.
If anyone is unsure what this means, try to pronounce the first part of the word like English "look".
That really depends on who is speaking. "lukter" is one of those words where the pronunciation can vary from dialect to dialect. I'm not sure what the standard pronunciation is, but quite a number of speakers pronounce the u in "lukter" as in "tur", "pute" and "lure".
In my dialect, the pronunciation is something between Norwegian o and u (very close to the double o in "look", if not exactly the same).
It means that it smells a moose. "Sniffing a moose" is "lukter på en elg" (implying that it is right next to the moose and practically or actually touching it with its nose), and smelling like a moose is "lukter av elg" / "lukter som en elg". "Lukter elg" is also possible, but ambiguous as it could mean both smelling a moose and smelling of moose, depending on context.
Only if you're talking about a bad smell. You wouldn't say "Det stinker rose". "Lukter" is the neutral term, and is indeed used in this setting. The most important sign of this use would be that the object of the sentence is without any definiteness whatsoever (Actually not a real object, but an adverbial use of the noun, telling how the dog smells, not what it smells). "Hunden lukter elg" vs "Hunden lukter elgen" or "Hunden lukter en elg". The first one would be translated as "The dog smells of moose", and the two others would be translated as "The dog smells the/a moose".
Yes and no.
A moose in America is the same as an elk in British English, whereas an elk in America is usually the same as a wapiti deer (wapitihjort in Norwegian), but also in English one could use the word moose of the main species of European moose and elk for one of the subspecies. To avoid confusion, it seems many Brits now also call Alces alces and all its subspecies moose – to avoid any more confusion than there already is. At least moose is more unambiguous than elk.
In Norwegian, the only correct word for a moose is en elg, and the American and Siberian subspecies are called amerikansk elg and sibirsk elg. An unspecified non-moose deer is usually called en hjort.
Just a comment. Wapiti is usually either called "amerikansk hjort" or called by it's native name, wapiti. Many foreign species are in Norwegian called by the native name, if they are not very "famous", like elephants and lions, and have been commonly known in Norway for a very long time. "Amerikansk elg" is not the same as "elk". https://no.wikipedia.org/wiki/Wapiti