1) How many decimal degrees does the equator span? - 360 dd
2) What about the northern- or southern-most
graticule line on the map? - 180 dd
3) What do these two lines in fact represent? - latitude(equator)
and longitude(meridean)
4) how many miles separate Washington, D.C. and
Afghanistan when crossing the Atlantic? - 7,000 miles
5) Is Alaska really bigger than Brazil? - No
6) What about Greenland? - No
7) How far is Washington, D.C. from Kabul now? - 10,100 miles
Just like any other projection, the Mercator projection distorts shapes and sizes of the true layout of the Earth's surface. The Mercator projection makes areas far from the equator much bigger then in reality. For instance, Greenland takes as much area on the map continent Africa, but in reality Africa's area is much greater than Greenland. Alaska takes as much area on the map as Brazil whereas it is far larger than Alaska. And lastly Antarctica appears as the biggest continent, but actually it is smaller than N America, S America, Eurasia, and Africa. Because of these vast distortions, this projection is not widely used as a good reference of the world map. Nevertheless, Mercator projection is still used commonly for navigation. This projection is still widely used for areas near the equator where distortion is minimal.

The Stereographic projection comes from geometry. It is basically mapping sphere onto plane. The projection is defined on the entire sphere, except at one point — the projection point. This projection preserves angels meaning it is conformal. This looks much alike to Mercator projection, and it also does not preserve the distance and area.
The Cylindrical equal-area projection is an “equal-area projection” as the name might tell already. As you look closely onto this projection, the longitudes and latitudes are perpendicular and they are (meridians) separated equally. By the nature of their construction type, cylindrical projections stretch distances east-west. My second equal-area projection is Bonne projection. Parallels of latitude are concentric circular arcs, and the scale is true along these arcs. Of you look carefully, the projection is maintaining shapes (areas) on the prime meridian. On this projection the distance is not preserved.

My first equal-distant map projection is Aitoff projection which displays the world on an ellipse. The basic idea behind the Hammer-Aitoff projection was first, to place the whole world in one hemisphere by the simple expedient of dividing all longitudes by two, then to compensate for that, stretch the map out twice as wide. My second projection is Equidistant Conic projection. These equidistant conic projections are well suitable for showing lands that shows some continues feature like temperature or elevation. It is clearly obvious that the projection was done by having North Pole as a center of conic projection, which created big distortion in the areas below equator, especially South Pole.