Does rain that falls near coastal areas contain salt?

Yes it could. In general, rainwater is rarely pure and distilled. it is often contaminated when aerosols (solid and liquid particles suspended in the air) in the atmosphere dissolve in rainwater or interact with low clouds. read more

In coastal areas, one common aerosol is sea spray, and salt is usually one of the constituents (google sea salt aerosol). Waves breaking along the shore tend to produce foam or bubbles. Sea spray then enters the atmosphere when bubbles on the ocean surface burst. read more

All of the salt inputs from rain, and rivers (and rivers have far more ions in them than rain does because river water is just rainwater that has percolated through soils) totals about three trillion (3 000 000 000 000 ) kilograms of salt per year. So, the yearly inputs of salts, although huge, is about one part in 17 million per year. read more

No. Salt does not evaporate with the water. Think about it - water that evaporates from the sea could fall as rain over land. If salt evaporated with the water then rivers & lakes would also be salty. Try a simple experiment. Get a saucer of brine & leave it on a windowsill. read more