Translation:Saturday we find a restaurant in the square.
I must admit that I'm not a native English speaker but I did ask around a bit (in a neutral way) to confirm my first impulse.
I researched (googled) a bit further: There is no conclusion. Some say that it's a UK/US difference (supporting your first statement as far as Americans go). One American never uses on the square. One Englishman finds in the square less awkward than on the square and suggests at the square as a third option.... meh
By the way I also learned that on the square may also be freemason code and/or mean honest and truthful.
Now back to the course.
No, there could not be a conclusion, because there are so many varieties of English and no centralized authority. No matter what you found in a Google search, there is likely to be some corner of Scotland or Mississippi or Jamaica or Tasmania or somewhere else that says it another way.
The OED is just a dictionary, like any other, though quite a good one. An American would be much more likely to look in Webster's dictionary to see whether his spelling or usage were correct. An Australian or Canadian might recognize some authority of the OED in theory, but he would certainly not see himself as bound to follow it. Moreover, there are a plethora of English style books, none of which look to any central authority.
this sounds a bit wrong. "piață" on its own means market.You would have to specify WHICH one to make it take the meaning of square.Like the square in the town center "piata din centru(l orasului)". It sounds a bit like you're gonna find a restaurant among people selling cabbage :))
A noun preceded by a preposition in Romanian is always definite, though (it would be translated into English, as here, with the definite determiner "the"). Any definite noun is the one we have been referring to earlier in the conversation or that the speaker thinks the listener will understand as a particular one. I can say a sentence like "The book is very important" and not specify "Charles Darwin's Origin of Species" is very important, because we have been talking about Origin of Species, for instance. In this case, it would be clear from the context which square, or indeed market, is meant. If not, the hearer can always ask "Care piață?"
The problem is that this sentence does not make sense in English. It suggests that perhaps this is a case where the present tense is used in Romanian but not in English, in which case adding extra words should be considered.
However, even that mightn't be satisfactory. Using the present tense suggests it's probably referring to the future but using the verb "find" suggests it's probably the past. The only context where I think this could make sense is a kind of constant present tense narration in a story (something like On Saturday we find a restaurant in the square and enjoy our meal very much. That evening we walk by the river and look up at the moon)
As you suggest, this kind of simple present is not uncommon in narrative. When I was using literary works in classes, our discussions would often include sentences like this, especially when I was emphasizing to the students that I wanted them to put themselves in the place of a contemporary audience. The other place I would expect to find a sentence like this is in narrating a schecule. E.g. Saturday we find a restaurant on the square (I still object to "in"), then we go to the theatre, and on Sunday we are expected to attend mass at the cathedral.