1. I guess you ask about the little ones that most of the religious Jewish men use (כיפה kipá), and not the big hats of the ultra orthodox.
Some use hair pins, and others probably rely on miracles.. ;-)
2. The color and the type can give some information about which stream or part of the Judaism they belong to. For example - the national religious will use a hand made wool one (on Saturday - white, on other days - various colors), the ultra orthodox - black velvet one.