1.) A "na" adjective is simply an adjective that needs a "na" after it when it describes a noun:
いい事 - "Good thing", いい is an i-adjective, the other type of adjective, it simply precedes the noun which it describes.
きれいな事 - "Nice thing", きれい is a na-adjective, it needs to be followed by a "na" when it modifies a noun by preceding it.
There are some other things to watch out for too, as always
Tae Kim is a good resource.
2.) There are no hard and fast rules; katakana is usually used for foreign words, and often for advertisements or as another form of italics. When crafting your own writing, write a word in hiragana unless you're sure that it's more commonly written in katakana.