If I wanted to, say, look for katakana in a block of Japanese text, or look for men and women of the same family in a Cyrillic passage (because Russian surnames change with gender), how would I do that?

It probably depends on the regular expression parser, but with Java's you can use \p{InKatakana} to match a single character in the katakana block (substitute Katakana for the name of whatever block you need, it seems to be case insensitive too.)

It doesn't matter you just use the UTF character.

Certainly for simple tests you can just iterate over the characters, yes. For anything more complicated having regular expressions is useful.