No, the first sentence which I wrote is not right. :) I just found that out:
“Ĉu vi vizitos nin dimanĉon?” is “Akuzativo de mezuro (Accusative of measure)” and here that means time (duration). Question words would be: “kiel longe?, (dum) kiom da tempo?, kiel ofte?” Source: http://bertilow.com/pmeg/gramatiko/rolmontriloj/n/mezuro.html
There also exists the accusative for “tempopunktoj” (I don’t know a good translation for this word into English). An example for this is: “Mi alvenos sabaton.” As both for measure and for “tempopunktoj” the ending is both times “-n” it is not easy to distinguish them. Question words would be: “kiam?, kiudate?, kiutage?, kiujare?, kiufoje?” Source: http://bertilow.com/pmeg/gramatiko/rolmontriloj/n/tempopunkto.html
So the question word here is not “When?” but rather “How long?”.
If you want to express a reoccurring event you would say “dimanĉe” as in “Ni kutime renkontiĝas dimanĉe.”
Regarding the preposition replacing: In theory you can always replace a preposition with “-n” as long as it is understandable. I often replace “al” as in this sentence: “Finfine mi povas skribi vin.” instead of “Finfine mi povas skribi al vi.” You have to pay attention not to make a double accusative as one subject can only have one object in Esperanto. So do not say: “Donu lakton min.” instead of “Donu lakton al mi.” Source: http://bertilow.com/pmeg/gramatiko/rolmontriloj/n/aliaj_signifoj.html