To answer the first two questions:
Being emotionally open to me means to on the one hand tell people about my feelings and on the other hand be understanding and empathetic of the other person's feelings. It definitely requires strength, but as you said later on, you can be rather detached and still be emotionally open. For example I might tell people I'm sad my grandpa died and not cry in front of them, just state the facts, and then react comforting when they start crying about their recent loss.

Being vulnerable, however, to me is not as you described it just helplessness and dependence. Being vulnerable means that if you are it with the wrong person, they can hurt you. For example, if the grandpa in the previous example died some horrible death and it just happened yesterday, this could be used against you. So, for these topics you'll be careful with whom you share. Being open about being a bit down today is easy, even if somebody taunts you over it, what do they really know. Being vulnerable on the other hand can lead to them using it to trigger you, to hurt you.

Vulnerability is more deeply intimate since when you are vulnerable with somebody, you signal that you trust them enough that even though they could now hurt you deeply, destroy parts of your life, whatever else, you believe they won't.

Vulnerability does not per se lead to dependence or helplessness. Yes, lots of people feel helpless about their trauma, or when they finally find that person where they can share all their issues, they become dependent on that. But both of these are not interchangeable with vulnerability. You can be strong, not show any of the pain that comes from the trauma and at least seem completely in control, yet talk about it, this is still vulnerable. Dependence, on the other hand, is something that happens a lot with certain kinds of trauma or when people can't deal with their emotions themselves and look to others to help them with that.

About self-soothing: bubble bathes and the like would not be my first example of this. You chose the example of "if somebody hurts you in a personal way after being vulnerable, would I be expected to self-soothe?". Let's go through this example: you share some trauma/personal thing and they start using it against you. You could get very angry about this. To not self-soothe would mean that you let this emotion consume you. You first yell at them in public, then go home, can't even concentrate on anything you're doing at home because you're so angry, can't stop being angry... you might also lash out repeatedly at the person and make their own life a living hell. I'm not saying that it's never okay to yell at somebody or even to take revenge. But being consumed by your emotions is rarely a good thing. Ideally, you'd probably tell this person they suck and you never want to see them again, then go home and have some way of managing your emotions that after a few minutes, you can concentrate on your fun evening instead of ruminating about this event non-stop. Maybe that would be a bubble bath or boxing, but it can also be just a few deep breaths, maybe five minutes of meditating...
This is not "expected", but it is beneficial to you. Being overly emotional almost never leads to good decisions, and after you've kicked the person in the curb, thinking about the fight for hours on end is not doing anything either. Self-soothing means you can deal with these emotions efficiently on your own. This is something lots of people learn how to do in therapy. Insofar it is "expected" at some point in therapy, because the other option is usually that you call your therapist whenever there's some bigger emotions, having them help you deal with it, and that is dependence, which is not actually a desired effect of therapy.

I'd like to add that emotional detachment can be a strength as you described it, as well as a way of self-soothing. If you get angry, manage to detach a bit from the situation and afterwards feel okay, that's good. It can lead to difficulties, however, if either you never show your emotions (relationship partners need to see how you react to things in order to know how to act) or if you detach whenever there's any issue coming up, because this will lead the person to believe that you are not invested in the discussion, so why should they even try.

Finally, I don't think you need to be very in tune with your "soft side" to be vulnerable, nor in tune with your feelings, though I think the second part is helpful. If you are not aware of how you're feeling about something, then it's difficult to judge whether you trust the other person enough with the information. Because what if you think it's fine, but actually it's really not fine. And then this other person knows this thing that you're actually not okay with them knowing. You can of course still be vulnerable, all that is really needed is sharing stuff that could be used against you, but you might later be uncomfortable with the fact that you did share. Also, if you are out of tune with your own feelings, you might not be sure that this person is actually trustworthy, which might lead to regret as well.
An example of vulnerability based in strength would be: let's say you have a problem with alcohol addiction and are recovering. Your best friend decides to organize a party for a few people including you. You tell them that you recently struggled with alcohol abuse, you're doing fine now, but being around lots of options for alcohol, people who drink and offer drinks to you is still very difficult for you and you'd like to avoid it, if at all possible. Then, you ask them whether it'd be possible to not offer any alcoholic beverages at this party.
In theory, your best friend could abuse this a lot. They could invite you to places without telling you there'd be lots of triggers for alcohol. They could offer you drinks whenever possible or even share the information with other people who are not well-intended. So, you're being vulnerable. You don't just keep this to yourself and somehow power through the issues described, you share your issues and hope for the partner to be understanding. Yet, you are not sitting there sobbing, going on about how you struggle with this and how bad you feel about asking this of them. You just stand your ground and explain your part in an objective manner.

I also have some thoughts regarding defenses, but that'll have to wait til later.