Kate, thank you for this thoughtful post on an important topic. In fact, some of your comments apply to many other places, but are especially important in New Orleans.
With respect to #1, the Census officially has plans to count the homeless or other people in temporary settlements. Whether this happens will be largely up to the Dallas Regional Census Center, which will oversee all the local offices in New Orleans. I don't see them listed on the website, but they're supposed to already have some local offices opened with the rest opening in the fall. Unlike local officials they don't care if a unit is "legally" inhabited, only if someone is there.
As for #2, the Census does have a "New Construction" program that will be particularly important to get new units. Unfortunately, they're leaving it up to local municipalities to participate - so advocates should check with their local parishes or the City of New Orleans. You have to register with the program by October, then send in the data next spring to be included in the Census.#3 is hugely important, we can only hope community education efforts help alleviate these issues.