I'll answer these questions for me, but it can vary and in terms of stress, it really does depend on how you manage stress and what job you go into.
Bit of a background for these questions. I'm integrated in a company, our UX team is currently a team of 2 and we look after all our business's products, UX as a whole has been part of the company for just under a year now.
A. Social is a little bit of a must with what we do. You need to advocate within your company (if you are integrated like I am), you need to give transparency to the other areas in the company so people know what you are up to, why UX is important, and how you can help them. People are generally more comfortable approaching you for help with ideation or designs when they know more than just your name and job position (and it can be hard to be included in everything so often this is a good way of staying in the loop). You want to instil trust, and show that what you do is actually really important. We use Yammer for posting up good articles that we've read on UX, and also sharing what we are doing. But we also ninja up posters around the office.
1. I'm definitely an introvert, but people at work wouldn't say that necessarily. I'm more an introvert who has extroverted tendencies at work.
2. What do you mean by face to face time? I'm around people all day, I'm on phone calls, or popping over to desks, in meetings etc. You generally get to know the people you work with, and even being an introvert, if you've got a company who's culture you fit in well with, and you get on well with your immediate team it can be fine.
3. It depends on your team makeup and job. I'm not normally the one doing the negotiation, unless I'm showing a design to a stakeholder, in which case you need to be able to think on your feet, so saying why you did what you did, the rationale behind it, and the different ideas you tried before coming to this one, why their suggestions are good (and you will either take a look at them, or why they won't fit for this design). But you do definitely need to be able to walk through your designs and rationale at least to your own team, so not pointing out "this is a button". You need to walk them through a scenario or story, giving context around what needs your design meets.
Now this one I think sounds scary, but it isn't that bad. If you have been spending enough time on the design, you should know it inside and out and be able to explain your reasoning. I also think this doesn't necessarily come naturally so it does require a bit of practice. I'm still working on this one! You do also need to be able to take criticism, as it is not always going to be constructive, and it is easiest when you don't marry yourself to a design.
B. Stress. As I've said above, it really does depend on your job and who you work with, as well as how you deal with it. Every job can be stressful, deadlines, working within constraints, having stakeholders who want something you know isn't a good idea... I'll use me as an example. I don't like stress, and I'm not one of those people who work better when they are running out of time. I like to plan and organise so that I don't get to that point in the first place. Never works. I'm having to learn that I can only do as much as I can do. With changing deadlines, iterating, and changing opinions things can get quite stressful, but just as long as you can get on and get things done regardless, then leave it at work when you go home, things should be fine.
So I guess I'd say stress levels fluctuate so average out to medium, it is often time based stress, and you just have to do your best with what time you have if you can't get any more.
Does this help?