Answering in good faith as someone recovering from homelessness, knowing this post is so severely downvoted and will probably be removed or ignored.

In your humble opinion, are the majority of the homeless people responsible for the situation they are in?

No.

For this and the rest of your questions there are 5 main types of 'homeless' and all categories below often find themselves into multiple of these categories the longer they are homeless.

Archetype 1, The Victim: Nearly all homeless technically fall into this category, but I'm going to define this as you did, 'victim of circumstances outside of their control.' All homeless start out like this. Either from being born mentally ill and no longer having care, losing a job, losing a house, running away from abusive parents, running away from other domestic violence, being a part of the foster care system, or getting addicted to drugs (most commonly through the opioid epidemic.) But to further clarify and deal with annoying people:

Archetype 2, The Mentally ill: American society specifically is not built to handle those that cannot help themselves. It is so violently against the chronically ill and mentally ill, that the majority of those suffering from severe illness of any type will end up homeless at some point during their lives (including 'couch surfing' as homeless). Most homeless people will eventually become mentally ill if they stay on the streets longer than six months. Given the lack of available reasonable resources to get out of homelessness, this is a large minority of The Victims.

Archetype 3, The Druggie: Drug addiction is a disease, a disease you are either genetically predisposed to, or not. It can start as a choice, but does not always start as a choice. Stopping is not a choice most can physically make. This, like all addictions, will only end when it is ended. Barring arguably divine intervention only hitting rock bottom and staying there can truly 'cure' someone of drug addiction. So once they reach the end of their grace with their loved ones and friends, they're still alive, but cannot maintain enough free floating cash to maintain a home (if they could even qualify)

Archetype 4, The Victim, but old: In many parts of the country you cannot get a job past a certain age, you will be discriminated against. And it will be done automatically in a plausibly deniable way. This gap usually exists between 55 and 62. This is the age you are most like to become homeless for the first time as of 2020. You get laid off, you get fired, you get constructively let go, you don't have social security, you don't have a good enough body for general labor, you will be discriminated against severely by pretty much everyone hiring... and then you end up homeless. And until you get your social security, you will stay homeless, as older people (before social security age) are usually at the bottom of the list for grants (specifically older white men have the least available options and programs to help them out of homelessness).

Archetype 5, (Rare) (Epic) (Legendary) The Actually Prefers Homeless: Easily the 0.001% of homeless people. These are never the ones you have ever seen on a broadcast or news report, except when they rarely get caught. They don't and won't ever fully fit into society, as they fundamentally reject the concept. Everyone else can and has been cured before, this is the only archetype that 'deserves' to be homeless, because it is genuinely the only thing they want in life.