1.
I dimly recall such a rule from the earliest days
You're right, except that it's carried through almost until today.
TW p. 68 (1st through 4th printings) says "In general, when a ’Mech falls while moving from one level to another, it drops into the lower of the two hexes." However, TW p. 59 says:
"Piloting Skill Rolls required because of movement ... must be made immediately following the action."
Can't have both. Then there was:
TW p. 68 says:
"To find the number of levels the ’Mech fell, subtract the level of the hex into which it fell from the level of the hex from which it began the fall."
It doesn't tell how you determine where you "began the fall". And if you always fall in the hex you arrive at (per TW p. 59), then all falls due to your own movement are 0-level falls. You "began the fall" in the hex you arrived in, and you fall there: it doesn't matter how many levels you changed or whatever.
I realized during the Manual's construction that BT has used this rule wording back to the 2nd ed rulebook (one of a few things that led Randall and/or I to ask how the hell that had been missed all these years). In the Manual and the TW 5th printing those legacy sentences have all been axed and it now states with certainty that falls always occur in the hex the PSR was failed in. This of course makes PSR timing an important thing.
2. DFA *is* among them. See p. 151. So no problem in this scenario.
3. "If a physical attack might cause displacement, and in doing
so interrupt another physical attack, the ’Mech with the lower
Initiative (i.e. the first to move) resolves its physical attack first. If
both attackers are on the same side, the controlling player(s) may
determine which attack is resolved first. If no valid target exists, the
attack automatically fails."