Is there a difference between sea and ocean in Hungarian? or are they both 'tenger?
Yes, there is a difference. Which is "Sea" in English, that is "Tenger" in Hungarian. However the "Ocean" is "Óceán". http://oceanservice.noaa.gov/facts/oceanorsea.html <- Read if you are interested. It's short and interesting. :-)
Is there a significant difference in English between "above" and "over"? Reported, but now I'm just really curious about it.
Not especially. They can mean the same thing, though they have slightly different connotations at times. To be "over something" means specifically to be directly above it. To be "above" something just means that you are at a higher height than it.
I suppose you have a point. Now I wonder if there is a difference in Hungarian.
we say "felett" or "fölött" (though as I've seen so far, duolingo only tend to use "fölött"), and they both mean the same thing
over can indicate direction, e.g. "the bird flew over the forest" would probably mean that the bird started in front of the forest, flew up so that it was higher than the trees, and when it got to the end of the forest, it flew down again. While "the bird flew above the forest" would mean that the bird was higher than the trees, flying around and around, but always with the trees beneath it.