Though I half hate to post this list now I'm getting people offering their answers, I suspect that process has run its course very nearly. (It took the threat of posting my answers to bring anyone out in the first place.) Anyway, these are the answers, some of which you have indeed guessed:
1. "Can you lend me a rope so I can swing a fellow out where I can get a better shot at him?" Buster Keaton, in Our Hospitality, has fallen in love with a woman he doesn't know is part of a family his family were feuding with in the Old South. His father and brother learn his identity while he is under their roof, so there's a problem about shooting him on the spot, but once they get him out of the house and running free, he's fair game. Keaton has fallen over a cliff and is trapped on a ledge when one of the brothers makes this request of a prospector with a well loaded burro.
2. "General--you go down there." As Grace guessed, Little Big Man.
3. "She's my sister AND my daughter. Do you understand--or is it too tough for you?" Evelyn Cross Mulwray (Faye Dunaway) in Chinatown. (This one was copiously guessed.)
4. "Why why why WHY was he wearing a ballet sssKIRT Charles?" As Grace discovered by technological means, a line from The Ruling Class. The Archbishop, usually referred to as Bertie, and played well past his considerable comic potential by Alastair Sim. Peter Barnes, the playwright, remarks in the commentary for the Criterion edition that the part as written in the play is funny, but as played by Sim it's ten times funnier. He turns a supporting role into a leading part simply by the exuberance of his playing. (This line in the play is "Why was he wearing a ballet skirt, Charles?" I don't know if this influenced Peter Barnes in developing the character of Carlos with his characteristic stammer in Barnes' next major play The Bewitched: "Why why why WHY do I ssssuffer?") Barnes adds that it's quite common in the theatre for people to turn a lesser part into a lead by force of presentation, but rare in film because editing tends to trim such flights--and in fact every version of The Ruling Class I've ever seen that was trimmed for length had much less of Sim's sheer manic exuberance as Archbishop Bertie.
5. "That's not a single malt whisky. It's some kind of a . . . polymalt!" (Corrected reading.) Doyle, the half demon/half human who becomes Angel's first assistant when he moves to L.A. on the series Angel (a spinoff from Buffy the Vampire Slayer). After mighty exertion he ask for a shot of single malt whisky and Angel gives him what's on the premises, which of course is a blended scotch. As is frequently the case on both Buffy and Angel, a charcter searching for a correct word and not finding it, comes up with a substitute which is comically/poetically apt.
6. "There was me, that is Alex" etc. This was generally recognized; the opening line of A Clockwork Orange.
7. "We're screwed."
"We're way past screwed. We're so far past screwed the light from screwed taqkes a billion years to reach us." An exchange between Dan and Roseanne Connor as the consequences of a bad financial decision sink in. A good number of people who've always avoided Roseanne would be surprised at how sharp, witty and literate the scripts generally are.
8. "Success to crime." A toast proposed by Sam Spade (Humphrey Bogart) in The Maltese Falcon.
9. "So these staged suicides of yours are for your mother's benefit?"
"No. (Long pause.) I would not say benefit." Exchange between Harold (Bud Cort) and his psychiatrist in Harold and Maude.
10. "C.K. Dexter-Haven. . . either I'm going to punch you in the jaw or you're going to punch me in the jaw."
"Perhaps we should flip for it."
Exchange between Mike (Jimmy Stewart) and Dex (Cary Grant) in The Philadelphia Story.
(Sorry Grace, not Groucho, but he's on this list.)
11. "So who do you like as the killer?" I'm sorry I don't remember the name of the assistant who says this to the Mexican police captain played by Charlton Heston in Orson Welles' Touch of Evil. See the restored print. Accept no substitutes.
12. "They have you shot twice in the tabloids."
"It's not true. Never came near my tabloids."
Exchange between Nora Charles (Myrna Loy) and her husband Nick (William Powell) in The Thin Man.
13. "Why do you realize if there were no closets, there'd be no coats, and if there were no coats there'd be no hooks, and if there were no hooks there'd be no fish and that would suit me just fine."
Groucho avoiding the subject of how he came to be in a lady's closet in Monkey Business.
14. "So get out there and lie like dogs and if Willow doesn't miff all her lines like she did in a rehearsal, this'll be the best high school production ever of Death of a Salesman."
As Grace guessed, Buffy the Vampire Slayer. Giles (Anthony Stewart Head) is directing a High School drama production in Willow's dream. (Very intricate episode involving Willow, Xander, Giles and Buffy in individual dreams which meld into a collective one.) I figured anyone familiar with the series, even if they didn't remember this line, would get it just from the name 'Willow'.
15. "So that ebola virus--that's really got to suck right?" Grace guessed The Outbreak, which I haven't seen, but I heard this line (and it's the only really funny line I've ever heard, though my knowledge of the show isn't encyclopedic) on an episode of Friends. Maybe they lifted it from The Outbreak, as they lifted the head engulfing turkey from Mr. Bean on another episode.
16. "Watch how you're driving!"
"Am I driving?"
Exchange between the Little Tramp and the millionaire who's his bosom buddy when drunk, but doesn't recognize him when sober, in City Lights. Charlie, in panic at the news, grabbs the steering wheel double handed.
17. "How do you say 'drugstore' in French?"
"Le. . . Drugstore."
Exchange between a pretty young American tourist in Paris and Jacques Tati's M. Hulot, in the movie Playtime.
18. "My my my. . . nipples explode with delight. My my my. . . hovercraft is covered with eels." As Grace guessed, John Cleese of Monty Python, impersonating a Hungarian trying to make himself understood in English with a phrasebook he doesn't know is seriously misleading.
19. "I'll give you exactly ten minutes to get your hands off my balls." The neo-Nazi Schillinger's response to what some might consider an overfamiliar gesture of reacquaintance by Ross, a prisoner he knew before, re-arrested and sent to Emerald City in the maximum security facility called Oswald Penitentiary (Oz for short), which is also the name of the series this touching example of tender human contact is drawn from.
20. "Try to break into my house. . . I ought to blow you away. I got to tell you the truth--the only reason I don't is 'cause somebody might hear me."
Dennis Hopper as Ripley, the title character in Wim Wenders' The American Friend. These are almost the first lines he speaks, and quite characteristic.