2. Is the noon Sun ever directly overhead in Los Angeles, California (34° N)? If not, on which day of the year is the noon Sun highest in the sky here? Lowest?

The Sun in Los Angels is never directly overhead, it is the highest on June 21 and lowest on December 21.

Explanation:

The Sun has a different effect and intensity at different latitudes. This is due to Earth's inclination which is at 23.5 degrees, meaning that the areas north and south of the Equator between 0 and 23.5 degrees are the ones that receive direct sunlight, while the rest of the planet doesn't.

Los Angeles, by being at 34 degrees North, is out of the zone where it can get direct sunlight. Considering it is in the Northern Hemisphere, the Sun is highest in the sky on the summer solstice in the Northern Hemisphere, on June 21. The Sun is the lowest in the sky on the winter solstice in the Northern Hemisphere, on December 21.