"Tisch" is singular. The plural of "Tisch" would be "Tische" (or "Tischen" in the dative plural).
"Auf" is a so-called two way preposition, which means that it is followed by either the dative or the accusative.
"Auf" is followed by the dative if it refers to a fixed location (e.g. Der Teller ist auf dem Tisch. - The plate is on the table).
"Auf" is followed by the accusative if it refers to motion (e.g. Sie stellt den Teller auf den Tisch - She puts the plate on the table).
In the sentence in the exercise, "den Tisch" is masculine singular accusative.
I think stellen refers to setting something upright, meaning you want the plate face up. I think in German "in a standing position" is different from English. Legen refers to lying on the table. It sounds funny to say I lay the plate on the table vs. I put or set the plate on the table.