If we look at "twice made dips", we say two times as there is first a dip, then a peak (rise and dip), and then the next dip. This is like when one hops the band gap: there is first a free wave, then one that looks like it dies out, but if it is still a bit big by the end of the gap, then it goes on to the next free wave.
No, not so fancy (do they arise from interference from the internal reflections?).
In standard tunnelling, one starts with a normal oscillation, goes to evanescence in the "tunnelling" regime, and then continues with oscillation again once on the low side of the potential; in double descent the test error goes way up (like the potential earlier) in the "tunnelling" regime, and then on the far side comes back down and then continues descending.