Did Germany produce ammunition with depleted uranium?

No, even according to the report you link the Germans did NOT create DU rounds.
It states explicitly, a few pages after the paragraphs you quote, that

This is the only German round known to have the restriction "practice firing prohibited." Why* Remember, German uranium was as rofined; it was not "depleted uranium" as we know it.

I am skeptical about the author's reasoning for it not being used on the western front, but his reasoning to arrive at the conclusion that Uranium penetrators were created by the Germans is sound based on my knowledge of the chemical and mechanical properties of the metal and its modern use in these applications.

As to Belgium having much Uranium ore, 1200 tons isn't all that much (the ore isn't very rich in metalic Uranium).
It was at the time a byproduct of the mining of Radium and Cobalt, so effectively industrial waste. http://ist-socrates.berkeley.edu/~rochlin/ushista.html

The American radium-uranium industry retained the monopoly for almost ten years before it reverted to Europe, this time to Belgium. In 1915 a prospector had discovered at Shinkolobwe in the Belgian Congo a deposit of pitchblende and other uranium minerals of a higher grade than had ever been found before anywhere in the world, and higher than any found since. The discovery was kept secret by the Belgian mining trust Union Minière du Haut Katanga which mined the rich resources of copper and cobalt in the region. After the First World War ended a factory was built at Olen near Antwerp, and the secrecy was lifted at the end of 1922 with the announcement of the production of the first gram of radium from the plant using the African pitchblende.

This attitude is difficult to understand many decades after radium has ceased to be extracted from uranium ores, and has in turn become a waste product with its presence a source of complication in the disposal of waste from the uranium mining industry. It is now practically worthless, having been superseded for use in radiotherapy by artificial radioelements created in nuclear reactors, especially by cobalt-60, which costs about one US dollar for the radiation equivalent of one gram of radium. During the 1920s and 1930s the Belgian rate of production was limited neither by the capacity of the Congolese mines nor by that of the Olen refinery, but only by the funds available to hospitals and the needs of the market for luminous paint. The Congo mine was closed in 1937, as by that time more than 2000 tonnes of ore containing 65 per cent U3O8 were stockpiled, enough for probably 20 years of world radium consumption.

This stockpile was transferred directly from the Congo to the United States at the end of 1940, and provided the initial supply of uranium for the American atomic bomb project. Meanwhile, about 1200 tonnes of uranium in various compounds stored at the Olen refinery was captured by the Germans after the invasion of Belgium in 1940, only to be recovered in Germany by US troops at the end of the war.

So yes, there was a lot of Uranium in Belgium, waste from their decades of Radium manufacture from ore mined in their colonies and shipped to the home country as ore rather than refined on site (which was typical of the way Belgium and France ran their colonies, stripping them of raw resources rather than creating manufacturing in situ and shipping out the finished products, as was done to a large extent by the Dutch and British.
http://ftr-wot.blogspot.nl/2013/05/solving-historical-mistery-help-required.html goes from the same source as OP, and lists some of his research into the matter, effectively confirming the existence of the munitions, but seemingly the rounds never entered full scale production.
Now, it has to be added that these rounds would not have been nuclear weapons, or even radiological weapons. Uranium as a metal is not very radioactive at all, it's just very good at absorbing neutrons, triggering a nuclear chain reaction and releasing energy.
It is however extremely dense, making it perfect for use in armour piercing projectiles. It's also pyrophyric, meaning it readily burns when it gets hot when exposed to air. It's thus an incendiary armour penetrator, very effective against tanks.
The resulting oxides are also rather toxic, similar to lead and mercury oxides, but anyone caught in a tank hit by one of these shells would have more pressing problems than the toxicity of the dust left behind by the burning metal.