Why is it called 'drift'? It seems to be simply an offset in the random walk, not making the rw 'drift' in any particular direction... E.g. if I set it to 500 instead of 0.5, the resulting rw's still have similar shapes, just with a different mean.

Am I right in thinking that this and the following formulas assume that the mean of the series has already been subtracted at some point? Otherwise, -1 < beta_1 < 1 still implies that the sequence tends to revert towards zero... Suppose the series is outdoor temperatures in Kelvin: then e.g. beta_1 = 0.5 will make the temperatures shrink towards absolute zero, won't it?

t-statistics always have a non-Normal distribution (except with infinite df). Does "nonnormal" here just mean "non-standard"? (The bullet-point above also raises this confusion: to me, "non-normally distributed" means non-Gaussian, but this is generally true of t-statistics anyway.)

Unclear: "bias" can't be defined as the expectation itself. The equation seems to give the expectation of beta1-hat without reference to the true value of beta_1. Maybe the equation is just for the bias (in which case the E(hat(beta_1)) bit is wrong), or maybe the equation is correct if the true value of beta_1 is 1?

What is z?

As above: it isn't itself an estimator (of anything useful), but minimizing it tends to identify the nearest model to the truth.

The criteria themselves don't estimate p. They are just penalised log-likelihoods. I think the text should say "can help us choose the optimal lag length p".