What was Mexico's participation during the World War I? How were German-Mexican relations at the time?

Mexico became a battleground for Germany and the Allies in the World War. In the beginning of the war Germany had the strategy of buying up as many arms and munitions in the US as possible to slow down the material support for the Entente powers. Mexico being engulfed in the revolution was an obvious choice for diverting the arms to. Felix A. Sommerfeld and Hans Tauscher were in charge of the execution of this strategy. By the way, the shipments Sommerfeld made were initially not free of charge as some have speculated. The US wanted Mexico to calm down and regenerate pre-revolutionary trade. The Entente saw Mexico as a crucial base for oil supplies. Mexico had the largest deposits in the world at that time. The British fleet in particular needed Mexican oil for its operations in the Atlantic.

So Germany bought domestically produced weapons and sent them to Mexico? Did that really disrupt government acquisition?

The intention was to slow purchases by the Allies in the US. That indeed worked to a certain degree until the US munitions industry expanded capacity from 1915 on.

Any suggested further reading on this?

A good book to check out is Reinhard Doerries "Imperial Challenge," a biography of the German ambassador Johann Count von Bernstorff. A great read is Price and Hollister (free download) "The German Secret Service in America." Also a standard is Barbara Tuchman "The Zimmermann Telegram." If you can wait another few months I will have a scholarly book out called "The Secret War Council" that will detail all German intelligence activities in the US in World War I with the most up-to-date sources.