Does anyone know if it's possible to approach and pickup cargo container without using autopilot? I'm thinking of playing without it entirely.

You can but you need to control all the thrusters and RCS manually. Quite possible just a little trickier. I tend to use the autopilot to get me close then I do everything on manual. :)

Looks like it's impossible.
Recently I triedto approach cargo via manual control. So despite hud telling me there's 0 distance to this container I couldn't grab then until I used autopilot.

it is quite tricky, it took me a while on manual before I could do it. Glad you got it working though, that's the important thing. :)

How does this work? Even with the autopilot I can't seem to pickup the cargo pods, the ship doesn't even stop after plotting course, is it supposed to stop on top of the cargo? 'cause my ship just reverses after arriving to the cargo pods in an infinite engine burn that I have to stop manually.

Yeah. It supposed to stop above cargo. Check if you have enough energy for maneuver. Sometimes autopilot autofarts because there's lack of energy to complete the task. Also note that autopilot cancels if you press any of the control keys (rotation, burn).

Once your ship stops you can access cargo in space via top right monitor. Cycle through tabs either via mouse (they supposed to show if you raise cursor to the top of the screen) or via tilda key. Also note that you need a mechanical arm attached to your ship (bought and sold at equipment) to actually grab stuff. (Dont forget that you transfer pods and not cargo itself so you will have to throw some pods if you're full.)

I have energy for days, the issue is, without any input, autopilot goes to the cargo pod, then just does a 180º turn, then just starts the engine and never kills it, I have to kill it manually (pressing w or stopping the burn) or it just goes, and goes, and goes...

I guess devs quacked the autopilot. I haven't been playing in ages, so I can't say for sure.

I think the autopilot zooming away is related to upgrading the components of the engine and giving it different performance characteristics that it doesn't 100% account for. I've found lowering engine power to somewhere in the 20-40% range before your autopilot starts the deceleration burn lets you reliably dock with cargo containers, derelicts, enter planetary orbits... Pretty much everything that isn't a station.

I've upgraded the primary engine and i have also the problem JDGuio explained.
I just try to reduce the power on the helm screen from 100% to 50% and then i retry a course. This time, the ship stopped like it should do every time.
I have had this problem when they do the "autopilot fix" a long tiime ago and i have stopped to play the game since that time. So maybe this bug didn't hit the dev.