"Also when you realize that something you said or did could be interpreted badly, what is a good way to solve it?"
You just say "Wait a minute, I'm not sure that came out right" and rephrase or redo.
Social awkwardness and INTP seem to go hand in hand. Shoeless mentioned low self esteem and lack of confidence. Here, conceptually at least, is a way to set those two things aside so you can at least function:
Get your introverted head out of your butt and become aware of others.
Wait, that didn't come out right....
The way to get past yourself is to ask others about themselves. Then -- and in the nicest, most socially helpful way -- it's not about you any more. Ask them questions. Instead of "How you doin'?" make it "what's the best thing in your day so far?" It's specific, but can have a lot of responses. Ask them what's the next big thing, good thing, bad thing coming up for them. Ask them anything. Deflect all questions about yourself with something like " I dunno, I'm hoping somebody else will give me some insight on that."
Just don't ask "Why?" too many times. "Why?" is an INTP question. It can annoy others sometimes, I have noticed.
MOST people, unlike INTPs, enjoy talking about themselves. Even others who start their personality with an I enjoy talking about themselves more than INTPs do. So, literally, consider yourself a companionable information extraction machine, just keep inviting them to open doors about themselves. Oh, and every now and then ask "How did you FEEL about that?" Apparently it's important.
Eventually, when you see what most people find to talk about, you can at least LOOK and ACT comfortable even if your brain is little seething wriggling toads. There are people who don't believe me when I mention my introverted nature; I can pass pretty well. On the other hand, just so you don't get the idea this is easy, I'm 61, so I've been practicing for a long time.
The other thing is you get more socially apt with people you've known for a long time. What I notice about many younger folks today is they don't have situations that naturally lend themselves to long-term relationships of even an artificial nature, so it's kind of rough. I went through 13 years of school with the same 35 kids I started out with in kindergarten, and realized proximity over time creates social comfort even if I never liked the times I was in a spotlight of some sort.
Just be patient with yourself. When it comes to socialization, it's like you've parachuted into a foreign land and don't speak the language. You'll pick it up over time. Meanwhile, you're going to occasionally do the social equivalent of saying "Your mother sleeps with her brother" when you thought you were saying "Your mother resembles her brother." Just remember the magic phrase: "Wait, that didn't come out right" when you see the puzzled, angry or hurt looks coming on around you.
