The apps I am using are:
- Learn Japanese Phrases (TheJapanesePage.com), these is a free and a paid version. This was my first app when I started learning Japanese. Recommended.
- JLPT study (Mathias Navne) - for learning kanji and words
- iKanji touch (ThinkMac)
- imiwa - an excellent free dictionary
- Learn me hiragana - writing
- Learn me Katakana - writing
These are not all writing apps. Of those that are, I don't know if they support active styluses. They work fine with normal styluses though.