The first one is because of the Vennbahn, a railway that was constructed by the Germans in the late 19th century to transport coal and iron between the industrial Aachen region and Luxembourg. At the time the path of the railway was entirely within German territory but after WW1 the areas of Eupen-Malmedy were given to Belgium and most of the railway ran through this area apart from some small parts which ran through land retained by Germany.

The Belgians argued that the entire railway was vitally important to the economy of the Eupen-Malmedy region that they should have full control over this railway and a commission made up of the victorious allies agreed and thus the path of the railway running through Germany also became part of Belgium. This lead to a the creation of the German exclaves that remain to this day.

The railway line itself became disused over the years and was eventually was torn up and is now a walking/cycling path. There was talks about returning the land to Germany but I guess they decided it wasn't really worth bothering with.

Not so sure about the second one, but there's a few weird bits of border around Switzerland that probably date back to the Holy Roman Empire or the Napoleonic Wars.

I'm not an expert or trained historian, just a guy who finds borders and exclaves fascinating and have read up about a bunch of them over the years. Read up about Baarle-Nassau/Baarle-Hertog for some more border fun.