I'm often told that I am the smartest person that people have ever met. Whether or not that's true, I can tell you that it's not like you would imagine it would be. Sure, I coasted my way through a M.S. in theoretical physics without spending more than an hour studying in my life (still working toward my PhD), but it disconnects you from the general population much more than it connects you to anything else.
Let me answer a few of your questions.
1.) The best kind of genius would be a social genius. Every single person alive wishes they were better with people, and having the ability to form bonds, and to work friends, and to get the kind of people in your life that you'd like there, as well as network to get to where you'd like to be, I'd call that the best of everything.
2.) The inside of the mind of someone like me, is a lot like what's in your mind. However, I have a clearer idea of it all, just from being able to think about it differently. And honestly, we desire order much more so than the general population. So, when things change in our daily routine it's difficult to adjust.
3.) Thinking about humans in general? I think of them as dealing with the same things as I do. I see them dedicate more time and effort into simple tasks than I, and wish that I were more like them in those ways, and in how they relate to others. I love the way that I can see what will make me happy in the world, and what I need from life, and just what it takes to enjoy the simplest of life's pleasures. But it would be nice if I could have that without having to think about it, or create the kinds of situations where I am controlling every aspect. It's fun, but it's tiring. Sometimes we all just want to go home, lay down, and have someone there to make us feel better; Someone to love.
4.) Spotting geniuses isn't hard. We stick out. But there are some in the normal population who blend well with us. People who appreciate the arts and the sciences, who are laid back and prefer deep conversation to a house party. Who would never drink for inebriation, for the sole purpose that our intellect is a defining characteristic.
5.) We know at a very young age we're better than everyone else, in terms of academia, but we are told not to put others down, or to gloat, or to point out that there are just some things we will always be better at. And that starts in the home. A good family upbringing is beneficial if nothing else to being intelligent. Having a stable environment, some kind of comfort within the household, and someone to talk to about things, are great at all ages and for all people.
6.) What makes me happy, is love (and, of course, every kind of cute thing you can imagine). I love flowers, museums, operas, shopping, dining, dancing, etc. All of it with someone I care about, and all of it in a family friendly setting. You have to change routines when you're smart if you're going to care about others. You worry about saying wrong things, doing appropriate things, or being able to come across as yourself. And so, at a young age you know you'll always watch PG rated movies, and listen to music without profanity, and just be doing something socially acceptable everywhere, at all times. Not to mention, it stabilizes love lives too. Never too much affection in public, but always able to be romantic, show that you care, and have open discussions with your lover.Clearly, I do have a bias toward the romantic, and others may have biases in another direction. The point being, we structure our lives, and make things better for us and those involved with us; as friends, as lovers, et cetera. There's no difference between you and us, besides the work you put in to get somewhere, or to make something work in your favor. And I guarantee all of us are envious of your commitment. After all, it's the work that makes it all worthwhile. :-)