The Hanzi Writer source code is released under terms of the MIT license. The MIT License is simple and easy to understand and it places almost no restrictions on what you can do with the Project. You are free to use the Project in any other project (even commercial projects) as long as the copyright header is left intact.
The Character data Hanzi Writer uses is from the Make Me A Hanzi project, which extracted the data from fonts by Arphic Technology, a Taiwanese font forge that released their work under a permissive license in 1999. You can redistribute and/or modify this data (in the hanzi-writer-data github repository) under the terms of the Arphic Public License as published by Arphic Technology Co., Ltd. A copy of this license can also be found in ARPHICPL.TXT of the hanzi-writer-data repo.