Regarding the first part of your question, I think your readings of all three sentences seem correct and idiomatic. They strike me as a bit casual, but otherwise natural. Maybe 1a is the hardest to find a context for; but I think it would be plausible to say "I'm looking for work now, and regret having gone to the cheaper school instead of the more prestigious school, so now I wish I had gone there."
I don't think there's a strong difference in meaning between 1b and 1c. The second clause may be in the past tense just because it sounds better.
Suppose that time 1 is last week, time 2 is yesterday, and time 3 is right now.
I believe you are saying that sentence 1b ("I would have preferred to go there") means it is now time 3, and at time 2, I wanted to go there at time 2. And you're saying that sentence 1c ("I would have preferred to have gone there") means it is now time 3, and at time 2, I wish I had gone there at time 1.
This distinction is possible, but in practice I would not put too much weight on it--it seems unlikely that the speaker is making a conscious distinction here. If someone said "I would have preferred to have gone to Harvard," I would interpret that as describing their past preferences about what they were doing at the time. Like, they've graduated now, but when they were in Uni, they wished they could transfer. But that's also how I would interpret "I would have preferred to go to Harvard," unless there's some stronger context to make the distinction between those two statements.
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Regarding your second example, 2A and 2C seem unnatural: it feels like the speaker is stressing that there's something they like about the feeling of having ridden a bike. (Maybe they get a "runner's high" or feel relaxed after exercise or something?) I don't think these work the same way as example 1.