You’re correct! Katakana is indeed used to write loan words. There are of course other use cases like names of animal species (e.g. you can write 狐 or キツネ for fox, and 兎 or ウサギ for rabbit) but generally that’s where you see them.
And yes, kanji was used prior to kana and the earlier versions of kana looked a lot more like kanji, but just got simplified as time went on.
Oh, and the word you were looking for is “radicals” for the components. c: