There's a difference between the trendy places that make an apartment building out of shipping containers (which is what you have as your picture) and actual slums.
While there were patents for shipping container living as far back as the 1960s, the first place to do it where it was widely documented was Armenia in the 1980s after an earthquake.
many of these ramshackle Armenian shipping container homes, which they call “domiks,” are still occupied by people who never got back on their feet after the quake, even though most of the containers have become rusted and leaky, and are located on public lands. A few years later, during the Persian Gulf War, the US military used shipping containers as bomb shelters and mobile prisons, and the idea spread from there. By 1998, Simon’s Town School in South Africa had built its new school building from 40 shipping containers at a cost of only $227,000. SOURCE
How it happens organically sometimes is this: disaster strikes, and people send supplies to help. They send it in shipping containers. Instead of sending them back, the people keep them to live in because they have no homes and they are better than tents. They are then stacked on public land, land no one really claims or a donated area.
Or it could be because of war--in which case they will start as a refugee camp, with a mix of tents and containers--and in this case, yes, it will be orderly, with stairs and everything, rather than rope ladders or something rickety.
As to structure--it depends. Are they actually doing paperwork? Or is this a slum? Because they are unlikely to even be wired up correctly if at all. Take a look at this solution to lighting in the Philippines
Know as well that the pictures I have provided are relatively new. There are disadvantages to container living (it's a hotbox with no ventilation or light), like rusting and people actually tend to use them as a base to build other, wooden structures on top of. Also, a flat roof is not a good thing, so in places where they've been there a while they tend to add a slanted roof with corrugated tin.
Who is in charge? Is there a landlord? A collective government? Is everyone squatting?
Who is in charge depends on the government and if it's a slum or something trendy or just a cheap way for the government to build housing. Same answer to landlord. They could all be squatting, or not, as you please. It's your world and your neighborhood.
Are there public areas? a wider "street" or plaza? Or is it just a residential rat maze to maximize living space?
Again, this depends on how and why it was built and where the containers came from.
Is it enclosed with only a few "gates", or is it porous with anyone coming and going?
This implies planning. This is really going to depend on what people need. They'll do what works.
I would research Hoovervilles. No two were alike. They grew out of the Great Depression. Do look at the link above. Below is a useful snippet of that article.
Most Hoovervilles operated in an informal, unorganized way, but the bigger ones would sometimes put forward spokespersons to serve as a liaison between the camp and the larger community. St. Louis’ Hooverville, built in 1930, had its own unofficial mayor, churches and social institutions. This Hooverville thrived because it was funded by private donations. It maintained itself as a free-standing community until 1936, when it was razed.
You've got to look closely at WHY and HOW your community of containers was built before you can determine what it actually looks like. That's up to you, you need to do what makes sense in the context of your story.
So, you know, they could be hipster housing and look like this: