Re: reversing cats
You are absolutely correct that all troops move, then the attacks begin. However, while attacks happen serially (fastest speed unit attacks, THEN next fastest attacks, etc) the movement happens in PARALLEL. All troops move at the same time at a rate proportional to their speed.
Example - taking an oasis (1100 field length) with max speed cav (1050 move). If movement happened in series, and the fastest unit always moved first (before any other unit moved), your max speed cav would race to the other side of the battlefield, take up position at 1050, and then all four oasis units would forward into your cav. The battle would be over in one turn (and you'd actually need to command, or your cav would hit oasis cav, then the oasis inf would hit your cav and do some damage). Even before the update, max speed cav (960) would have still gotten hit by inf (1100 - 150 = 950) on the first turn during an uncommanded oasis fight in this (fictional) scenario. So I'm fairly sure this is never the way movement worked, and that nothing changed with the update.
What actually happens in this example (or any battle) is your cav and all other units move at the same time, but the rate of their movement is dependent on the unit speed. One way to calculate the point on the battlefield where two advancing units will meet, assuming no other units get in the way, is given by:
Defender movement distance = (distance between units) / (1 + (attacker speed/defender speed))
Attacker movement distance = (distance between units - defender movement distance)
There's a cleaner way to express that, but it's easiest to understand that way. Therefore in the oasis example, on the first turn your max speed cav will move about 855 distance before stopping at the defending oasis cav... DESPITE their actual speed of 1050. The oasis cav moved about 245 while your cav were moving. This is an easy one to check - go take an oasis!
In the case of a BACKWARDS moving unit, you have to think about it a little differently. The ADVANCING unit and the BACKWARDING unit will both start moving at the same time! However, the advancing unit will STOP when it reaches the backwarding unit. The backwarding unit will continue to move until it's movement distance is exhausted, or it hits the back wall of the battlefield. Therefore... if the backwarding unit can't move far enough backward after the forwarding unit stops, it will get hit.
To calculate where the attacking unit will stop when advancing on a backwarding unit:
Attacker position = (attacker initial position * defender speed - defender initial position * attacker speed) / (defender speed - attacker speed)
(If you plug numbers in here and you don't get an answer that fits between the two positions, it means the attacker never catches the backwarding defender)
Therefore, it is ALWAYS possible for a backwards-moving unit to get hit, but ALMOST always impossible to set it up correctly, given all the uncertainty in positions and speeds.
Annoyingly, and counterintuitively, it is obvious that the closer a unit is, and the faster it is... the LESS likely it is to hit a backwards moving unit!
There's an easy way to prove this to yourself. If you have 100 speed, and max marching and shooting techs, take off your horse and manual and send some catapults into an oasis. (20 cats into a lvl 5 oasis is a perfect bet here.) Move your cats forward on turns one and two (target inf to preserve oasis cav), wait them on turn three (target cats), then backwards them on turn four. The cats will get hit by the cav despite moving backwards! And here's the best part - if both cats and cav survive that encounter, move your cats backwards again on turn five - this time they WON'T get hit by the advancing cav!
Erm... If you do that, post your results, will you? I could use the corroboration.

Thanks for reading! And if you find a way to use this that is actually useful, let me know. It's just too hard to get this to work in a real battle. But at least it explains the confusion regarding whether or not reversing cats 'works'.