Not likely. Where are you? Are you barefoot? Is the water being dirtied by animal or human fecal matter? But not generally in the USA.
Probably not. Rainwater would not carry a parasite, so, unless it was contaminated with river water or some other standing water, no.
Unlikely. Hookworms can burrow into the skin on your feet from soil if you are barefoot, but just stepping in rainwater, if you have shoes on, even if your shoes are submerged and your feet soaked is not a likely scenario.