I suppose it's embarrassing for other people to correct me, but not to correct myself. So if I noticed my mistake before anyone else does, I don't care if I have to publicly correct it. I just dislike others doing the correcting for me. Though I tend to not speak about something I don't understand well in the first place. I don't like looking ignorant.
It differs. I would do whatever is more likely to get me the most practical, efficient and accurate results depending on the situation. Sometimes it means I need to ask someone I consider knowledgeable but other times I would rather find my own way. Usually the latter.
I'm not constantly thinking about it, but I'm aware of it.
I actually handle myself very well in moments of crisis. More so than most people.