Does this mean eating by the water, like alongside the river or lakeside? I'm not sure what this Romanian sentence is supposed to convey
This is like you don't go ashore to eat, but stay on board/boat/ship/whatever. Or you go for a trip by boat/steamer/whatever and say that you will not eat in advance, because you are going to eat on board anyhow. We don't really say it so, we will use "pe barcă", etc., but I think Duo selected this from a word data base, that is why it came out this way.
Can this sentence mean something like the meal that is prepared on water/using water, instead of being prepared on oil, for the fasting period for example. If in general you use oil in the pan to prepare some vegies, but instead you only use water? (If not, how would you say it? Hahaha I know I'm annoying with questions :D)