My question is how to wire the two appliances. The oven comes with a
four-wire copper cable. I suppose the bare wire from the oven should go
to the bare ground wire, white should go to the white-striped neutral
wire and black and red should go to the two black wires. Are the two
black wires in the wall interchangeable? If not, how do I know which
one goes to the red from the oven? Why are there four wires in the
first place?

The cooktop, on the other hand, has only three wires -- red, black and
bare copper. Why no white? How should I match up the three cooktop
wires with the four wires in the wall.

I realize I need to use antioxidant in the wire nuts when connecting
aluminum to copper. Any other precautions needed?