"Sabaton mi iros nenien."
Translation:On Saturday I will go nowhere.
sabaton = on (this/that) Saturday
sabate = (on) Saturdays
You will do this only once, not every week.
Fine, but the whole this-next thing with days of the week is heavily based on culture.
This is mostly true, but not followed by all speakers. I generally follow this distinction, except when it would make my Esperanto extra clumsy.
To denote "On Saturday" meaning just the upcoming Saturday as opposed to "Sabate" which would mean "On Saturdays" or "Every Saturday".
Time without a preposition needs to be in the accusative. The o-form marks the subject of the sentence. (La onklo rigardas la onklinon.) Unless you have a linking verb there is only one subject group in a simple sentence. (La onklo estas ŝia edzo.) The o-form follows many prepositions. (Mi venas el Parizo.) Some sentences have got a “second” object in the o-form. (Mi faras vin avo.)