Ok, too many posts to answer individually, but the short story is kinda this:
The DU in a sabot round is basically a long sharp metal spike with fins at the back. Not unlike a crossbow dart. Penetration being a function of kinetic energy vs surface of impact, using an 120mm barrel to put all that energy into a thin and heavy rod is causing a massive increase in penetration. (The padding around the rod is called the sabot, btw.)
The main thing you want there is a material which is hard and dense. Tungsten was used in older rounds, but DU basically beats it. As a bonus, DU is also ductile. Which doesn't mean you could draw it through a hole into wire at home, but at the immense forces involved in an impact against armour, it does basically tend to squeeze through that initial hole rather than, say, shatter. And if it does fracture, DU tends to fracture at an angle, so basically you've still got a sharp rod going through armour. That's what's sometimes called "self-sharpening".
When the round goes through metal, it is braked a lot. Kinetic energy is lost. As energy can't just disappear, it has to transform in to something else. In the case of friction, that something else is heat. Even through relatively thin armour, at least the surface of the dart and some of the armour it went through will melt and come out the other side as a spray of hot molten metal. Through very heavy armour, you can basically have the last inch sliced through more by a jet of superheated molten uranium, than a solid rod.
Again, here DU has the advantage of sheer weight. A denser liquid is still going to have an easier time going forward through that armour.
As that spray of molten metal and hot little splinters comes the other side, it burns in air. The vast majority of metals do that, actually. That's why a flintlock musket worked, for example: shaving iron splinters with a flint wedge caused a shower of burning iron splinters. Uranium does it too, and the old Tungsten sabots, or even WW2 iron sabots did the same. Parts of the broken armour do the same.
(Which cooks the crew and detonates ammo and fuel on board.)
Note that although this is often mis-represented as burning while going through the armour, that is actually false. It doesn't have nearly enough oxygen in there for that. And at any rate, that's not why it stays sharp.
The main problem really is with that spray of burning uranium the other side. It causes a lot of fine dust of uranium (and iron) oxides. And if the tank then goes boom, it can get spread around a bit. Or if kids go play in that destroyed tank, well, it can be bad for their health too. The oxides _can_ be absorbed through the lungs. Some of those oxides are partially soluble too, so they can get into soil and ground water too.
The main problem isn't with radiation, it's with it being a heavy metal. It will indeed do much the same damage in your system that lead would. Or that tungsten would, if we were to return to pre-DU penetrators.
Comparisons to the lead in a bullet, or measuring radiation levels for crates of ammo, are misleading though.
The lead in a bullet doesn't (partially) turn into a cloud of lead oxides when you shoot it, or you would see some real health problems from that one too. And measuring the radiation in an ammo crate is misleading because that's not the problem, and that's not the situation where the problem happens.
That said, I don't think it would be a very large problem, as basically there weren't that many of these rounds used in the first place. Of course, again, if some kid actually goes playing in a destroyed tank, he/she can get a bit more of that dust than their fair share.
I also don't think there's all that much we can do about it. For better or worse, even if we went back to the old Tungsten penetrators, they would still cause as much heavy metal contamination. Possibly even more.
The only realistic solution is, well, to avoid ending up having to use them, i.e., to avoid going to war. And I'm all for that, actually. But if the feces hit the ventilator and push came to shove, you have to use whatever works best for winning it. That means a bunch of toys which can be hazardous to the health of everyone there. There is really no way to make war pretty or safe.