Does "would" in "would do so" denote repeated actions in the past?
Yes, I think you're correct.
And does "would" in "would not be characterized" imply the first conditional as in "If I had enough money I would buy a big house"? [/quote]
Yes, I think it denotes something contrary to present evidence (the 2nd conditional, not 1st). However I am using the word "evidence" extremely loosley here!