Heya!
One weird thing in Canadian historiography is a tendency to talk about "the west" without BC (Sarah Carter's Aboriginal People and Colonizers of Western Canada to 1900 is an example of this). Which, you know, whatever, yes, the prairies are also west of Ontario, but really most of the country is. Anyway, this has led other historians to follow Jean Barman, whose quip that BC is "the west beyond the west" became the title for her seminal book on BC history.
One moment in BC history that resembles the "wild west" of cowboy movies is the Fraser Valley gold rush. A huge influx of gold panners to lands that Indigenous peoples had not ceded under treaty meant that tensions were high; there were deaths on both sides until an uneasy truce was forged.
There's a lot of sources on this, but you might want to especially check out Dan Marshall's thesis at UBC: http://webcat2.library.ubc.ca/vwebv/holdingsInfo?bibId=2310307
Yes and no. There was an unsettled west, but not really a wild west. The Minister of the Interior under Laurier, Clifford Sifton, aggressively courted Europeans to come and settle in western Canada. But it was federally sponsored, well organized, and directly led to the creation of Saskatchewan and Alberta as Provinces in 1905. It was a system of settlement that offered free/cheap land for immigrants that were part of the long, long history of Canada having far too much land and far too few people.
The wildest part of the Canadian experience in this area (I'm being very liberal with the world "wild") is the treatment of Chinese Canadians during the late nineteenth and early twentieth centuries. There are countless cases of boney (sic) legged goblin Chinafolk (I'm paraphrasing Rudyard Kipling quoted in The Organic Machine, Richard White and a couple other sources) . Good reading in this area is White Canada Forever by Peter Ward and almost anything written by Constance Backhouse (specifically Colour Coded). Plus there was the struggle to deal with the rapidly expanding electrical needs of an emerging economy (Fish vs Power, Matthew Evenden).
But yeah, pretty lame if you're looking for a Canadian Wyatt Earp. Obviously I'm glossing over the Louis Riel rebellions, which were brief rebellions and not an establishment of a "wild" west.
I'd make the argument that the Canadian West was wildest during US prohibition when there was a LONG undefended border that the Americans couldn't possibly hold all the liquor out. Canadian cartels worked with American cartels and there were fast cars and gangsters. (Booze, Craig Heron; Boats, Booze and Billions, CW Hunt).
Sorry I sort of wandered. The short answer is, if you're looking for an American West in Canada, it didn't actually exist. But it isn't like there wasn't anything going on and the Canadian West has an interesting story of its own.
hi! you may also be interested in this earlier post