Why are ESTJ's so attractive to INTP?
A combination of "opposites attract" (like any combination of opposite letters/functions), shared sense of humor (Ne-based usually), and the Thinking-dominant mind-meld, which I have experienced with every Ti-dom and Te-dom I've ever met, for reasons unknown to me.
What are your organizational skills like? I know stereotypically, Te dominants/auxiliaries are supposed to be pretty organized, but of course stereotypes aren't always true.
My answer is probably about the same as every other ESxJ's: Pretty good, but could be better. Perceivers tend to think I'm super organized, and I'm middle of the road when it comes to Judgers. I do really enjoy organizing, though. I like optimizing systems.
Is your dominant Te fuction pretty much a device to implement your Fi values? Is Fi like a driving force of right & wrong in the background?
Yes and yes -- and Si is Fi's copilot. Which is why the dominant-tertiary loop, for ESTJs, is leaping from unimportant task to unimportant task, without any sense of direction or prioritization at all.
What were you like as a child? Were you the confident, outgoing, all around good student, like I picture young ESTJs to be?
I was pretty much Hermione Granger. So yes.
What do you think is the biggest misconception about your type? Why do you think that is?
There are two, IMO:
1) that ESTJs can't think critically about everything and are going to be stuck in their ways forever -- some of this is based in fact (i.e. meeting ESTJs who aren't terribly intelligent and/or are generally closed-minded), and some of it comes from Keirsey and his ilk.
2) that all ESTJs are domineering. IMO this stereotype is more likely to describe a particular sort of unhealthy/medium-healthy ESTJ, most likely a 1w2, cp6, or 8.
My old ESTJ roommate was a psychology major with a concentration in social work (which I never would have guessed based upon other things I observed about her, if she hadn't told me). Do you think that's an unusual college major for an ESTJ, or could you picture yourself, or other ESTJs you known, taking an interest in that kind of work?
I've been interested in a line of work that is very similar to that in a lot of ways: the priesthood. I will most likely not seek out that career path for a variety of reasons, most importantly the fact that I don't think I could function in that position without suffering from constant burnout. I could envision ESTJs being great at either of those jobs, if they learned how to manage their emotions more effectively -- probably with some sort of mindful pseudo-detachment.
& Do you really care much about strangers opinions of you? Or do the opinions of those close to you only really matter?
I'm not sure how much of this is being social-first (re: enneagram), but I care a LOT about this. I care more about what those close to me think of me, but I also have been known to care about the feelings of total strangers. Some of those feelings are based on rationality -- for example, the idea of having a "good reputation" presupposes that people you either don't know at all, or don't know very well, speak highly of you behind your back. But a big part of it is that, deep down, I want to be liked, and I want to be appreciated.
What do you think of people that are rude in public?
It bothers me when people are rude, regardless of whether or not they're in public. As the saying goes, "The true test of a man's character is what he does when no one is watching".
Are you more realistic & matter of fact, or do you still try to take care of the people's feelings around you?
More of the first, but when someone I care about is upset, I do try to take care of their feelings. But the way I try to take care of their feelings is by fixing the issue that's causing the bad feelings. I'm not naturally good at active listening, or expressing empathy -- though I have been known to feel very strong empathy for my friends and loved ones.
Is it like you feel a pull telling you to be productive?

Understatement of the century.
Do you have any sort of specific feelings if you put something off? Do you ever procrastinate, or do you generally get started on things immediately?
If I'm stressed, I put things off. The specific feelings are mostly guilt, as well as inward-focused rage for letting things get to that point.
Where can I find gay ESTJ guys?

Grindr? I'm the wrong person to ask.