"Ela toma água com sal."
Why is, "She takes water with salt." wrong here? It would be unusual to drink salt water, but people do take it for medicinal purposes (like netti pots). I see it like, "I take cough syrup. (also a liquid), where it would be unusual to say, "I drink cough syrup." (which would sound strange, and the person likely has an problem or addiction.)
I would think it would be similar to saying, "I take an aspirin" instead of "I eat an aspirin." (which would be unnatural English).
The English use of "take" is as a dosage, and the Protuguese form of a dosage, as I can only assume from Spanish, is probably tome. In Spanish we say "Tomé jarave" if you take cough syrup, or "tomé una aspirina" if you have a headache. Still, your logic would apply.
Does "água com sal" have a different connotation than what in English is rendered "saltwater?"
For me, there is a little difference between água com sal and água salgada. I would say that in água com sal, you or someone somehow put salt in the water, but água salgada may or not be salty because of your or someone else's action.
For example, I would never say that sea water is água com sal, because it's naturally salty. Sea water is just água salgada.
As a native speaker, I understand that in the context of the sentence, the woman took some water and made a mixture with salt, and then drank. If the sentence was "Ela toma água salgada", I could not say where this mixture is from.
beber = to drink tomar = to drink, to take
"Eu vou tomar o remédio" = I will take the remedy. "Tome a pílula" = Take the pill!
there's actually no difference. They just sound better in certain situations but they mean same thing.