So, at 3:40---what precisely is the course? It's not an oval, it's not a figure 8--what is it?

Slalom: a timed race (as on skis or in an automobile or kayak) over a winding or zigzag course past a series of flags or markers broadly : movement over a zigzag route.

Closed loop zigzag?

Actually it varies every event. The co-driver has a map of the route through the channels and waives his hand in front of the driver, pointing the way as they go....it’s a bit like rally racing but too loud to speak the directions so they point.

Do the drivers get to review the current race map beforehand or is it a complete unknown? How much and what kind of prep does each team get regarding the current course?

Good question. I can’t find it in the posted rules, but if it’s like rally racing only the navigator would get to see it beforehand.
I’m fairly certain there’s not a practice round, so round 1 would be the drivers first look at the day’s course.

Confusing as hell if you ask me. I don't know where they're going, but they're making great time.