Hi Penthesilea...thanks for introducing another interesting topic. Here are three observations for consideration:
1. The tattooed lady:
One possible explanation for her inclusion is that, through her, Ang Lee is indicating ways in which society has changed since the late fifties or early sixties, especially for women. This woman is decorated in ways which earlier would have been thought outlandish and unfeminine yet she is not being shunned. Indeed, she seems to have a boyfriend by the way she is dancing and, in that way, is now part of society.
Perhaps Ang is also suggesting that the same is true of gays and society but of that I'm far less sure.
2. The Basque:
I imagine you want to keep discussion to the characters in the movie and not the actors who played them but, if not, there's an extended interview with David Trimble, the actor who played the Basque, on an excellent site called FindingBrokeback.com. If anybody hasn't heard of this site before now, do check it out. It's well worth while.
3. The salesgirl in Monroe's grocery:
Iy looks as though the shot you have is only half of that scene. At least, I've been looking at it on StripedWall - image 1808 - and there the other half of the frame is occupied by Ennis and is two children. In this shot, the young lady, rather than looking bored, is looking up at Ennis and his two children with friendly interest. Presumably, as Alma works in the store, she would have met Ennis and the two kids before. By the way, I do appreciate this movie's attention to detail. The beehive hairdo the young lady is sporting is absolutely right for the mid sixties.