I’m glad you started this thread, because I had kicked around starting a similar one as a result of the thread you mention (posting a link, below, to the place in the thread where the antihero discussion started).
Despite there being plenty of definitions of ‘antihero’ to be found online, I think there is a lot of uncertainty as to what an ‘antihero’ is, and lots of blurry distinctions to be found.
For example, in the thread I linked below, @Lucas_Jackson mentioned Travis Bickle in ‘Taxi Driver’ as an antihero, and when I protested, cited Paul Schrader himself saying he wrote Travis as an antihero as well as numerous other cites considering him the quintessential antihero. I conceded the point, but it still doesn’t feel right to me. I think of an antihero as someone who generally does the right thing, despite using morally or unethically unsound methods to do so. Travis Bickle is a seriously unhinged individual who was about to kill a Presidential candidate when he was scared off by Secret Service agents, and only became a vigilante hero by killing the pimp and other bad guy as kind of a consolation prize. ‘Accidental hero’ maybe, but not quite ‘antihero’.
I think of someone like the Deadpool character, or maybe a Dirty Harry as a classic antihero. The ends justify the means.
I’m currently doing a rewatch of Dexter. Midway through season 2, I’m trying to decide whether he’s an antihero or just flat-out villain. Yes, he’s a sociopath without normal human feelings or emotions who has an urge to kill, but he has the self-reflection and strength of will to stick to his ‘code’ and only kill other serial killers. He’s actually good to his friends, family and coworkers. Sure, it’s an act, at least to some extent, but who among us doesn’t put on an act in life at least a little a bit, at times?
Anyway, to answer the OP’s specific character questions:
Robin Hood
Anti-establishment, ‘fighting the power’ hero, but pretty much unambiguous hero.
Shrek
Sherlock Holmes (as depicted by Doyle)
Reluctant or flawed heroes.
Khan
Don’t remember his backstory very well, but I’d say mostly villain, but with some blurred justifiable motivations.
The Joker
There’s a million iterations of this guy, but not a lot of hard backstory, so I’d say your basic chaotic evil bad guy.
Professor Snape
William Munny (from the film ‘Unforgiven’)
Draco Malfoy
Don’t know enough about these characters to judge.