-- Why didn't OMT ever teach Jack a thing or go see him ride?
I think John Twist, probably because Jack was an only child, wanted him to stay on the ranch and make it work. Encouraging him to ride would have meant the end of his ranch.
-- What did he know or suspect about Jack? How about Jack and Ennis? How about Jack and Randall?
I think John Twist knew that Jack was not the marryin kind from an early age, and figured - in a practical sense - that two men would be ok for the survival of the ranch. Old Man Twist expressed disgust - not at Jack having a man come back here with him - but at the fact that Jack's dreams came to nothing.
-- Was he a mean SOB through and through, or was he genuinely grieving Jack (not mutually exclusive, acutually)?
I think John Twist was purely a practical man, and grieves more that the ranch will die, but probably genuinely wants Jack buried here on the ranch that Jack could have saved.
-- Was he homophobic?
No, John Twist viewed sexual and spiritual things as separate from the person's ability to be a productive unit in the survival of the community. He judged a person by his/her ability to be an economic unit. If Jack had told his father that Ennis and Jack would turn the farm into a landscape painting studio, John might have expressed his anti-artisitic "homophobia". However I think John's sexual views about hetero or homo habits were purely practical. Don't ask, don't tell.
-- Why didn't he let Ennis take the ashes?
John Twist sees no meaning in the ashes of Jack, and probably cannot understand the effect on either Ennis or Jack. He certainly has no perception of Jack being more at rest on the Mountain.
-- When he insisted Jack be buried in the "family plot," what did he mean -- was that an allusion to what we think of as (anti-gay) family values, or simply an assertion of control, or something else entirely?
John Twist sees no meaning in the ashes of Jack, and probably cannot understand the effect on either Ennis or Jack. He probably wants Jack to stay here on the ranch which Jack could have kept up and made a go of.
-- Ennis protectively shields the shirts when walking past OMT in the kitchen. What if he hadn't, and John Twist had seen the shirts? Would he have snatched them from Ennis' hands?
These shirts have no meaning to John Twist. To him they are mere rags that could be used to wipe off some dirty work area. I think If/when Mrs. Twist died before John, he would have quickly gone out and found a housekeeper/wife with little emotional reaction. And the new wife could wear Mrs. Twist's previous clothes with no reaction from John Twist. I think John represents a purely practical human survival mode of life.
-- How does story-OMT differ from movie-OMT? Can you imagine movie-OMT participating in the peeing-on-Jack scene that was in the story but omitted from the movie?
I think movie Old Man Twist would not have put Jack on the woolies, looked out to Jack and his peeing, or encouraged him to do/be anything other than a hard working ranch hand. His interest in Jack having a wife would have only been to reproduce and provide another generation to keep the ranch alive, and bringing home a man would have been ok if they worked hard and kept up the ranch.