Question

Which map projection is most useful for navigation, especially near the equator. Explain

The map projection that is most useful for navigation would be the Mercator Projection because near the equator the shapes and sizes of features are correct.

Answer 1

I agree.

Answer 2

Yes, the Mercator Projection is very accurate, and mostly on the equator. You are completely right Sue.

Answer 3

I do not agree.

The important thing about the Mercator projection is that the direction of one point to another, say New York to Fastnet Rock south of Ireland is accurate on the chart even though the earth curves significantly between points. (angles on the sphere are as you measure them on the flat chart)
This is called a "rhumb line " course and it works.

It is not the shortest course, which is along a circle (called great circle) which is on a plane containing New York and the Fastnet and the center of the earth. However to sail a great circle course you must change compass course continually (break it up into a lot of short rhumb lines). That is in fact done by ships on long trips.