My instinct says all of these are in "Mind." However, I think the main issue that's keeping you from being able to assign a Domain here is that these aren't really "conflicts," per se. These are bad things, sure, but there's nothing preventing all four of these men from simply repressing these negative emotions forever. Let's say I add a Limit to the first one:
A man who won't ask the woman of his dreams out on a date for fear of rejections must discover his courage before she moves away to another state.
Though perhaps I've cheated a little here, because the key part isn't the Timelock, but the phrase, "discover his courage." By saying this and not, say, "must come up with a method to woo her," I've leaned more heavily towards Mind.
How about if we make an Antagonist instead?
A man so afraid of being critiqued that he has not submitted a short story for his fellow writing students to critique finds himself in the bet of his life when a rival author dares him to win the Hugo Award within the next five years, or risk losing everything.
Now I've tried to bias it more towards Activity.
How about the Influence Character?
A man frightened of dealing with strong emotions, avoiding processing the death of a lover, finds those emotions immediately in turmoil when the woman who received his wife's heart in a transplant tries to be a part of his life.
This one... might be in Psychology? The MC Throughline would probably be in Mind, since the IC Throughline is almost certainly Situation. (Also, apologies to David Duchovny.)
...Shoot, I want to do another IC one.
A man fearful that his hobby will come between him and any relationship finds himself in a life-or-death situation with a cross-dressing co-hobbyist at a convention gone horribly wrong.
Does that sound Situation-y? Also, now I really want to write this story.