Not an expert in the field, but some rough guesses...
1. Depends on how it was done.
If it was an injected isotope, then traces of the isotope remaining in the system could well still be giving off radiation when the bodies were discovered. But that's not something you'd know until you used a Geiger counter.
Similarly, a radioactive gas or something could remain in the system to give off radiation.
Just plain exposing someone to radiation shouldn't cause them to be radioactive.
And if the bodies have been in the river for a while, some or all of the radioactive traces remaining could well have been washed away.
2. Radiation poisoning could leave radiation burns. An experienced, sharp-eyed officer might be able to spot the difference from regular burns. But it'd be hard. Not many people have experience with radiation burns. And the water of the river would have washed away dead skin cells, bloated the bodies, etc. And if the poisoning was from the inside out, I'm not sure what would show on the outside.
3. Depends on where they are when they figure out what's going on, what's available, etc. Really, if they have a Geiger counter handy, odds are there's already an expert around. Also, if the bodies were pulled out of the river, they'd probably be on a boat, no? Not much to do there. Try to keep your distance, I guess.
4. If the bodies are dangerously radioactive, I guess you'd need the guys in hazmat suits. In a big city... probably some special police unit related to the bomb squad. Not really sure.
5. If there are still radioactive traces in the body, then they should be identifiable by the exact nature of the radiation being given off.
Otherwise... the location and nature of the radiation burns would tell you how the exposure happened, if not the exact substance. Again, it'd be harder given the dunking, but external exposure vs injection should be relatively obvious.
6. Possibly. Depends on how radioactive the substance is, how long it was in the system, etc.
It's also possible that the injected substance would be poisonous in other ways, like a heavy metal.
It should be noted that kryptonite is, traditionally, only mildly poisonous to humans. In the comics, Lex Luthor wore a kryptonite ring all the time. He did eventually develop cancer in that hand, but only after years of continuous exposure. Certainly, none of the humans we saw on the show seemed to be affected by it. Though it's possible that injection could lead to more severe consequences.
For more info, you can check here:
Radioactive Contamination Radiation sickness/poisoning
