The D in Depleted (U-238) has nothing to do with it's radioactivity but that it's not fissile. Fissile U-235 is not too badly radioactive either (4 billion vs. 0.7 million year half life i.e. 77% more radioactive 0.5^(0.7/4) / 0.5).
We don't make depleted uranium to have less radioactive uranium (naturally occurring uranium is < 1% U-235). We have DU because we made nuclear bombs.
Interestingly the Ruskies have made DU arms far more expensive now with their breeder reactor (U-238 is fertile).
2) DU is an alpha emitter. I would bath in a bathtub made of alpha-emitters and sleep in a bed of alpha-emitters.
However, Uranium shatters making dust. I would not want to breath, eat, drink an alpha-emitter. It's a heavy hitting He ion that will knock the socks off anything in it's short path.
Not to mention U-238 becomes Th-234 with a half life of 24 days (very radioactive) with beta emission (ouchy!). There'll never be a lot of Th-234 (U-238's low radioactivity) but it'll all decay into you (Th-234 small nuclear half-life and large biological one).
So U-238 effectively decays in your body as a an alpha and beta!
What happens when you blow up DU? Gets scattered throughout the local environment.
3) ...Low biological half life
That's only relevant for disaster tourists. For people whose environment has been seeded with the stuff, the biological half life is completely irrelevant as it is replenished as you eat, breath and drink. An equilibrium concentration is therefore established.
Therefore, environmental half-life is far more important than a biological one.