# Equal area projections with different area results in ArcGIS for Desktop?

Using ArcGIS, I have to calculate areas of huge polygons all over the Pacific Oceans betwwen 20N and 30S. I have been trying different Equal-areas projections (Cylindrical and sinusoidal for example) and found different results for the area claculation.

For example, one polygon is having a surface of 1'604'176 km2 with Cylindrical and a surface of 1'605'483 km2 with sinusoidal...

So my questions are:

Am i correct to use Equal area projections for calculating areas? Should i be using a different type of projections (equidistance...)?

How can you have different results between the projections and which one should be consider best?

At last, using an equal area projection, I discover that if I break down a big polygon into 6 smaller polygons and i compare the sum of the areas of the 6 smaller polygons with the area of the big polygon, i have a difference between the values (difference of 60Km2 for a polygon of 1'600'000Km2). How is it possible?