For the "word trees" my main source of information is the English-language Wiktionary, to be found here. There I use the Wiktionary by manually looking up words and entering info manually into my database as needed. This should be covered by "fair use", and I give links to the pages used anyway.
The display of info from numerous and arbitrary Wiktionary pages by the etymological text analyzer here and the cognate checker here is based on the Creative Commons Attribution-ShareAlike License that Wiktionary grants.
Both features use automatic, programmed lookup of Wiktionary pages in the background. However etymology.ch is not a so-called "live mirror" of Wiktionary, as explicitely prohibited for all Wikimedia properties (see here): Each word is looked-up only once and the info stored in a local database for all further look-ups.
Furthermore, the crawl-delay directive mentioned in the site's robots.txt file is respected: There will always be a delay of at least 1 second between two such automated accesses to Wiktionary.
The software on the etymology.ch server (written in C#, ASP.NET MVC 2) uses a C# port of the Porter stemming algorithm, under a BSD license. Details see here.
It also uses word lists from Princeton University's WordNet, under the license that comes with WordNet 2.1. Details see here.