Ik zet het glas op de rand van de tafel.

In Dutch you distinguish putting things down by orientation:
• leggen = lay something flat (horizontal).
• zetten = set something upright (vertical).
A glass normally stands upright, so you zet het glas. If you laid a book flat, you’d say Ik leg het boek op de tafel.

Here op is a preposition meaning “on,” not the separable verb opzetten (“to turn on” or “to put on”). You can test it by asking a location question:
Waar zet je het glas? → Op de rand van de tafel.
That shows op introduces a place. With the separable verb opzetten, the meaning would be different (e.g. Ik zet de radio op = “I turn the radio on.”).

rand is a feminine noun meaning edge or rim. The phrase rand van de tafel literally means “edge of the table.” In Dutch you link two nouns with van (of), placing the van-phrase after the head noun:
head noun (rand) + van-phrase (van de tafel).

• op de rand = “on the very edge,” suggesting it’s precarious.
• aan de rand = “at the edge,” more like next to or near the border.
• op tafel = “on the table,” anywhere on its surface.
Choosing op de rand highlights that the glass is perched on the table’s rim.

Yes. tafelrand is a compound noun (“table edge”). You can say:
Ik zet het glas op de tafelrand.
Using rand van de tafel is just a more explicit two‐word construction; both are correct.

Yes. For a yes/no question swap subject and verb:
Zet ik het glas op de rand van de tafel?
With a question word like Waar, place it first, then the verb, then subject:
Waar zet je het glas?
Op de rand van de tafel.