Does anyone know the proper term for Japanese characters, and where I can find a good site to practice writing them? Thank you.
There's hiragana (ひらがな), katakana (カタカナ) and kanji (漢字). Dn my experience, the web hasn't been very good at teaching kanji. I think books and writing by hand are the best resource for that.
The simplest form of writing is called hiragana. The Japanese invented this. Katakana is used for words which come from foreign languages. Kanji originally came from China but the Japanese adapted it a bit to suit them and kept some of the sounds they make as well. Kanji is mostly used for words which the Japanese use quite a lot and hiragana fills in the spaces between them. On Duolingo, you mostly learn hiragana because it is the simplest, and a few simple kanji.