The piece of skin you're referring to is called a frenum (or frenulum), and it's totally normal. It's basically a bit of skin that stops bits of your body from moving too far. In this case, it stops the foreskin from sliding to far back. You'll find another one in your mouth, on the underside of your tongue.
As for the second part of your question, please, someone step in an edit this if I'm way off the mark, or putting forth the wrong ideas.
It sounds to me like you're describing asexuality, which is absolutely no weirder than any other sexual orientation. People who identify with the asexual orientation experience pretty much what the rest of us do, eg: the same emotional experiences, physical attraction to others, etc etc. The only difference, however, is that asexual individuals just don't feel the need to act on any attractions sexually.
While there are some people that will tell you asexuality is a type of sexual dysfunction, remember, bisexuality and homosexuality were both thought to be sexual dysfunctions too, but in reality they're both perfectly normal.
You might want to check out this website for a bit more information (http://www.asexuality.org)