How would you translate "A wall doesn't solve anything" (present time, not future)? Is it "Zed' nic neřeší"?
Yes, that sounds like a possible translation. Colloquially, I think, one could use that even for the English future (not accepted in the reverese exercise).
Very strange phrase, maybe its a phrase in Czech, but in English, no. 'A' wall is not going to solve anything (Trumo's wall!), but a definite article, 'the' wall outside a Trump context doesn't make sense.
"A wall" is also accepted. As a native AmE speaker, though, I don't find anything odd about the use of "the wall"... it simply indicates that a particular wall is being discussed. And, for all we know, the sentence's author may have had Trump's wall in mind! :-)