BasicCAT is a desktop app and users can have shared translation memory and term bases by running a server program. Collaboration is also possible using git and GitHub just like the way OmegaT does.
The teaching platform(source) is discontinued as I am not a translation teacher who has the need. There are a few commercial translation teaching platforms in China. The first one only has a Chinese interface.
- shiyibao: http://www.shiyibao.com/
- 51chaoqun: http://study.51chaoqun.com/, which is based on my teacher Yu Jingsong's CATTP project (Computer-Aided Translator Training Platform, see the English paper: http://tac-online.org.cn/en/tran/2009-10/13/content_3183297.htm)
They all have functions like peer review, error classification and automatic scoring, but not integrated with a CAT environment.