In general, I'm not a fan of setting people up, but I do think it's ok to invite two people to a group activity and let them see if they hit it off for themselves...without any interfence from me save the original orginization of the activity. I think, too, that I'd be more willing to set up someone that is "happily" single vs. "unhappily" single. As the second group of people tend to put too much pressure on potential relationships and aren't that much fun to be around. I wouldn't set up a friend with someone who is generally unhappy about anything. I do agree that those who are "happily single" because they don't want to be in a relationship shouldn't be set up at all.
To answer your second question, I do think the method matters. Putting them in a setting with a bunch of other couples is awkward at best. But, I wouldn't think it be nearly as awkward to invite them to a group activity, introduce them to each other, and let them go from there. I also think, depending on the people involved, that it would be ok to set up a blind date or double date if everyone involved were interested in doing so. (This is something that I personally would never do though).
Finally, it's definitely over the line to insist on setting someone up and intervening in relationships when one or both parties has expressed disinterest (or indifference). It's definitely a MYOB situation.