Hm, well. Before I say anything, I'll preface this by saying 1) I'm young enough that my functions still change around a lot, 2) that because of social pressures I've had some weird function development, and 3) I'm not great at function-oriented introspection.
Ok, now that the "I fail" disclaimer's out of the way...
First, I relate a lot to what Jennifer and, to a lesser extent, blankpages said. It's not that I don't care, it's just that in some situations my caring is a much more disconnected way of caring. My way of comforting is "Well hey, look at this though. This means this, and that means that [good thing here] will probably happen," or something else of that nature.
The thing about little kids and the mentally ill I also agree with a lot. It's not that I dislike them, I just...don't know what to do with them. My Fe really can't operate without lots of backup from Ti and Ne, and without the intellectual connection that they like to form through Fe I'm pretty much lost with regard to how to deal with people.
I agree too about the "if you wanted help, you should have asked" thing. If I'm not talking with someone, I'm usually not really paying attention, so of course I didn't notice that you were doing something you might need help with.
And again, I agree about being able to chat with people fine, but having no clue what to do next. I have a ton of what I call "school friends," people I get along with at school but never do anything with outside of it, but almost no real friends. That's not because I don't want any, but just because I still can't figure out how you move on to being friends.
I've also never got the "INTPs have no emotions" thing. I tend to feel things strongly when I feel them, it's just that when I'm engaging Ti-Ne I'm really not aware of how I feel (does that sound weird? I dunno, it's just how I am. I don't notice how I feel unless it's really strong, or I've got nothing else to pay attention to).
I also do have trouble differentiating between a request and a demand. I guess because I usually avoid asking someone to do something unless I absolutely need them to do it, I assume that when someone asks me to do something, they absolutely want it done, rather than just a "Oh, if you have a chance, it'd be cool if you could do x for me, but if not, it's not a big deal." I could hear that sentence, and still somehow feel like I have to get it done.
As for how my Fe operates in its own right, I'll give an example.
When I have a problem with a friend, I'll try to avoid dealing with it as long as I can (if I don't think I'll like the outcome). Eventually, I try to confront them over it. If they listen, all goes well, I keep control, etc. However, if they try to avoid what I'm saying, I reach a tipping point. If they don't reverse course quickly, I lose it. What happens is my F controlling Ti, I guess. I don't shout or anything. I very quietly, very coldly, rip apart everything about them that I can think of that I have a problem with. Afterward I feel absolutely horrible, but once that tipping point is reached, I just don't care whether I'm being horrible or not, because as far as my Fe's concerned they deserve it.
Also noteworthy: except in those reactions, my Fe almost never has anything at all to do with my Ti. If I'm using Fe, it's virtually always in combination with Ne.