Ok, I am going to break this down bit by bit bc I want to show a few things to you.
"Sometimes, I wish I could have someone simply tell me that I'm doing all right. That they are proud of me "
I think it is normal to want affirmation and a little big of "love", but you can start with self love. Do you love yourself?
," and that I'm not a bad person, that the bad things in my childhood weren't my fault.…"
First, it really is not your fault -and I hope you know that deep within yourself no matter what others say because others can be hurtful at times. Next, the only "bad people" in this world are those who refuse to learn from their mistakes and instead prefer to embrace them to the point they don't card who they hurt (the only possible exception here are those who have ASD). So unless you consider yourself to fall under that category - you need to know you are not a bad person.
"A lot of the time, I really would just like to feel safe and protected and understood."
This is something you generally only get from parents, spouses, or pets.
"If someone walked up to me and were a stranger, to be honest, I would not want to talk to them."
This is understandable, but at the same time if you want people to be accepting of you, you need to be accepting of them. That does not mean you have to be the first to speak or that you can't be shy or cautious. It just means you should be willing to accept a possibility this person means you no harm and only wishes to be your friend.
"But I would hope that they would be patient with me, because it takes me a very long time to open up. And I can't articulate my needs, because I don't know what they are… "
There is no reason you should need to feel rushed to disclose anything of even that you need to disclose anything at all. This person is to be your friend, not your counselor, so what and how much you choose to tell them about you is up to you.
"I am really struggling to think of something specific I would want a person to say to me. I don't trust anyone, so I stick to small talk or jokes. If I can't do that, I walk away rudely. Maybe I don't expect them to like me. And I expect myself to make sure the conversation or the person doesn't hurt me."
It really sounds to me like perhaps you have low self esteem and are perceiving others as judging you, with the judgement you have passed on yourself. That sense of judgement stops you from socializing. Maybe I am wrong. That's just how it sounds to me.
I think you should give yourself a chance. Show yourself the love and understanding you crave. Once you do, you will find socializing easier.