Are there any open-source typing tests?
Not open-source, but free and web/online is TypingTest.com which seems to work pretty well based on a couple of tries. It is a Java application, so you need your browser to have Java support turned on. Is access to source a requirement, or is ‘free’ the important part? If you need open-source programs with native Windows support, SourceForge has TypeFaster Typing Tutor which includes typing statistics and lessons, though not specifically geared to tests. It’s beta status, updated within the past year, and has a current 88% activity percentile for SourceForge projects — which is mediocre as active SF projects go, but given its limited appeal, not so bad. There’s also the popular and mature Tux Typing on SourceForge, but it appears very child- and game-oriented. A polished interface, but probably not in the manner you wish.
If you key off the custom word list feature and drop the open-source/free req, then Typing Tester should work. Not expensive for a personal copy, but you have to request a quote for network licensing, and frankly the software has a minimalist, early 1990’s look based on the screenshots. A free downloadable demo is available if you have any interest. As a second non-free choice, TypeMaster Pro looks slicker and is cheaper than Typing Tester, and also has statistics, network licensing and a downloadable demo. The education version implies you can use your own word list, although the exact phrase is “customizable typing tests” which I suppose could be interpreted to mean something else. No personal experience with either, including the demos.