I read that these are the best mods for the visual part of COP, is that true? Can anyone explain to me how it works and which one is for which part of the game?

As I understood AtmosFear is a mod and Absolute Nature is an addition to is. Why the first one is from 2010 and the second one from 2017. Also, their size worries me, one is 100mb another 600mb.

Both are complete, fully tested and covers the whole game?

Still, 2010... It was so long ago...

The latest version of Atmosfear is from 2011 yes, it modifies the weather to be more realistic and allows you to set weather patterns per map (such as default weather and how long weather cycles last). It also allows you to control how often blowouts and psy-storms happen and how bright or dark nights are. Installation instructions come with it or can be found on the moddb page.

Absolute Nature changes a lot of models and textures for all the trees and other plants. It also adds many trees to the levels. There is also Absolute Structures, which features higher-res textures for buildings.

Installing these mods is not difficult, though you may notice substantially worse performance after installing them.

You could also try the ABR mod 1 (he's working on 2.0 now, which will have more gameplay changes. Version 1 is mostly just graphical improvements.) This mod has all the graphical improvements I mentioned above already included. For me the performance with ABR was better than when I installed the graphics mods individually.
https://www.moddb.com/mods/abr-mod