Yes, this expression also exists in American English.
"To eat off a plate" would be in contrast to "to eat out of a bowl" or "to eat off the table/tray/floor" or "to eat out of someone's hand". You say "off" or "off of" ("of" is optional) for flat things and "out of" ("of" isn't optional) for rounded things, because food is "on" as in "on top of" flat things, and it's "in" as in "inside" rounded things, so you use the opposite words since you are removing food from those places.
You can also just use "from" in all cases: "to eat from a plate", "to eat from a bowl", etc. I don't know if Duolingo accepts this, but people will easily understand you.
You can also say "drink through a straw", "drink out of a glass/bowl/etc.", and "drink off the floor/table/tray" (if a liquid is spilled on a flat surface). You can use "from" with all of these too