The article mentioned locals claiming to have pushed down a car one night ... No idea what volume of synthetic DNA would be sensible here, but I can imagine it'd mass less than a car.

Almost every living thing contains DNA (the possible exception being some viruses if you consider them living).

I imagine leaves / fish / spit / what have you fall into the water all the time.

The only synthetic part of it is the sequence - on a molecular level it's exactly the same as naturally-occurring DNA.