You need to read the car manual, some automatics have two oil pumps, and the manual describes how to push start, and warns about tow starting as you can easy run into the tow car. I remember my mate having a problem starting in a USA army base and asking for a push, and the guy said yes and proceeded to jump into car to push him with it, but we don't have bumpers like USA cars and the car was damaged as a result.
With no second oil pump need to disconnect gear box to tow. Use to remove prop shaft, but how with a front wheel drive I don't know.
As to trailer towing in the early days of 3 speed automatics they would over heat towing, but the newer vehicles the weight limit is often higher for automatics, Jaguar XE 1500 for manual and 1800 for automatic for example, the automatic is an eight speed box.
The Ford Fiesta, DAF, Honda Jazz used the infinitely variable transmission, and often got better MPH than manuals, no way could you work out road speed from engine noise.
The Morris marina I had told you how to use the automatic gear box for engine breaking, and it would not change down until safe to do so, but the Mini automatic (4 speed unusual back then) had free wheel in first and would wreck the engine if put into second at too high of a speed.
CAT 769 you could select the highest gear it would use, seem to remember 16 speed.
So each automatic box is different, you need to read the instructions for your car, not any other car, although the early boxes were a development from the Wilson epicyclic gear box, know as a pre-select, common on old Daimler cars with a fluid flywheel, the fluid flywheel was replaced with a torque converter, and these also varied a lot with 2:1 to 4:1 reductions, some with clutches that locked the flywheel over a set speed. Some cars actually had an automatic clutch, the old 2CV for example. Even the Smart car uses a friction clutch, very like the Honda step through motorbike.
The old automatics could change down at the most inappropriate time, kicking down while going around a roundabout is not funny as rear end brakes away, but with 8 speed boxes you don't notice the changes, with the Rover 3500 the standard mode was 2 speed only, had to select drive 2 to get first gear, today often three selections, eco, normal and sports, even the old Toyota Yaris had an overdrive on the 3 speed box, making it really 5 speed, although overdrive could be used as an automatic selection, it could also be manually switched off, to give more power for overtaking.
The Jaguar XE can be driven like a manual using paddles to change gear, the old Honda Jazz also had paddles option even though it had an infinitely variable transmission, so it is a case of read the instructions.
Some times reading the instructions can be wrong, the Vauxhall Agila I had warned against using mobile phones in the car, not just driver, anyone in car should not use a mobile phone, I know why, some Vauxhalls the mobile phones could disable the ABS brakes, but the Agila did not have ABS brakes. The old Vauxhalls with ABS you had to use an outside aerial on any mobile phone, but phones today don't have that option, so only option is to put phone in flight mode.
I see the problem, often you don't get the instructions with second hand cars, my wife got stuck on a hill with our Kia Sorento, she had another 5 gears to go, but did not know where the switch was for low range.
