Yup.
That’s correct. The effective population size (Ne) is the size in some population genetics model that generates behavior like that seen in the real population. (What you think Ne is can depend a lot on how you estimate it. Humans have a very large variance Ne, but a small Ne as estimated by heterozygosity. If that’s the case, it’s not clear to me that Ne is really a useful concept.) Usually the effective size is smaller than the census size, often a lot smaller. It’s possible for it to be bigger, however, at least in the case of subpopulations that are nearly isolated from one another.
Swamidass is certainly correct on several points. Estimates of past Ne are point estimates of the most likely value at each point in time, which is quite a different thing from a lower bound on the population size. Ne also represents a kind of average population size over extended times, rather than a precise estimate for every generation; this makes it rather insensitive to very short bottlenecks. Whether this kind of thing is enough to allow for RTB’s model depends on what exactly is in that model.
Yeah. A short bottleneck of 20 individuals 200,000 years ago might well be undetectable today (I’m not sure, but it seems plausible), but that’s still a factor of ten off from a single couple.
Correct.