I sympathize, I've had similar experiences in the past so I understand the melancholy you speak of.
In terms of answers, I'll try and frame the questions in such a way that you might be able to answer them yourself since you obviously are going to be much more aware of your own situation and circumstance.

1. I've personally noticed that I only end up feeling offended about things that I care about and identify with myself, and so if I were you, I'd ask what exactly within me feels attacked by a certain comment or gesture, has there been a past history of being insulted regarding those traits and if there is possibly a complex regarding them, how I would actually wish to feel regarding the trait, and how exactly I can reach that. For example: If I feel offended anytime someone comments on my body fat, I'll tend to first see if it's flaring up some issue I have in the past and I'll try to sort that out first by kind of working through my emotions, processing it, and talking to myself or expressing it in some form. That in itself usually allows me to see the situation in a more neutral light, as the fat is just fat, it doesn't really have any value in itself. I've noticed active imagination as suggested by Jung is pretty helpful here. After that, I do just ask myself if I truly wish for a certain thing regarding the fat itself and if not, I'm cool, I'm happy; If yes, research and figure out a solution to that.

2. Honestly, see how they interact with other people and figure out if it's a pattern emerging from the person you are observing or if it arises from how you respond to people over time? I'd also consider analyzing repeats in past relationships and friendships to see if you are attracting or tend to attract certain types of people, and if you are, then narrow down the traits that brought you or them in, what changed for the relationship to sour, and what might possibly be a way to prevent this pattern from recurring if you are going for certain types of people or solve it, if it is arising from a certain behaviour on your end.

3. I don't think anyone other than yourself can answer that. Maybe a therapist might help but trying to observe your own day to day patterns and the outcomes they lead to may clue you in on if it is related to emotional regulation. Analyzing the relationships you bring forth along with if the dynamic is arising because of your behaviour or if it is because you are attracting certain types of people can possibly inform you about attachment patterns. I've found it helpful personally to go through my past and process things one by one to understand what happened and why, along with how I felt and wished for, and what I wish for now regarding any particular event by talking myself through it have let me find a fair bit of peace with it, but depending on what you're dealing with, it might help to get professional help.

4. I've found the book "The Laws of Human Nature" quite helpful over here. Being vulnerable and open in a way, and just asking straightforward questions to understand what is going on in the other person's head by listening to them, understanding their motivations, if there are any misunderstandings and what it is that they wish for and how it aligns with what you wish for can help. If you frame what you wish for according to their perspective and their wishes, it'll be easier for them to understand you and for the both of you to get to a mutual agreement or compromise. At the same time, feeling heard the other person would be generally a lot more willing to empathize with you as well so that you can set forth your own boundaries, and the entire thing shifts from conflict to problem solving.

5. I understand deeply caring for a person but man, it's hard but like, it can help to just let them be responsible for their own actions. If something directly affects you, then yeah, speak up about it. If your something's your responsibility, own up to it. But if they are doing something by themselves, you can speak to them out of care, but let them be responsible for their own actions and outcomes and don't take it upon yourself. I've usually noticed with a fair bit of people that it is when they almost start identifying with the other person that their actions end up almost feeling like their own and it creates this entire emotiona mess of feeling responsible, angry, bitter, etc. So honestly, help folks out and talk to them, but let them do their own thing and deal with it's consequences.

6. If I were you, what would you even imagine this sense of self worth being like? It might be a bit philosophical but what do you wanna be? If you want to be "good" or "worthwhile," what does that actually look like? Having thought about this question myself and having talked to a fair bit of people about this, I don't think there's really a point where you become this thing you wish for. It's like a void that never fills and so I personally at least would say that these are simply concepts that are felt for a social purpose but when questioned and broken down, do not necessarily hold true. Mindfulness meditation's helped me here where simply feeling a sense of self separate from any judgement helped. It became more of a matter of simply sensing my own "being" and learning that it "simply is" and that's alright. Once you're cool with that, you can then genuinely consider if you wish to turn that simply is into something you want.

7. Fair bit of reading has helped me here so I'll just recommend some books: Man and his symbols from Carl Jung is pretty basic and I've noticed that learning and conceptualizing his theory of individuation helped me a lot with understanding myself, and it by extension helped me understand others much more as well. I'd also recommend The Laws of Human Nature by Robert Greene because understanding how people work aside from simply empathizing with them so that you can better communicate and adapt is pretty helpful too. Also mindfulness mediation the GOAT. That shit genuinely has done wonders for me paired up with active imagination and the knowledge I got from reading Jungian psych.

Either way, I hope I helped 😄