Couldn't we say " Der Rock liegt auf dem Tisch " ?
That's what real Germans usually say
Agreed. I've been taught that way.
Could "Der Rock ist am Tisch" work as well?
"am" (an dem) means "at the table" like - Wir sitzen am Tisch -- We are sitting at the table. You must use "auf" when discussing items physically on the tabletop.
Could you also say, "Auf dem Tisch ist der Rock?"
In theory, it just sounds kinda funny. The subject usually comes first. If you said "On the table is the skirt." in English it also communicates the point, but nobody would ever say it like that.
What about "aufs"? o.O
Aufs is a contraction of "auf das", so in this sentence it would be wrong as der Tisch takes the dative article dem.