Folding dry ingredients into the cake batter: at once or in 2/3 portions, does it make a difference? The following is my go-to sponge cake recipe:

6 eggs
2 and a half cups flour
1 cup oil
1 and a half cups sugar
1 cup milk
2 and a half tsp baking powder
cardamom and saffron

First I separate eggs, then I cream egg yolks and sugar. I add oil and mix well, then I stir in lukewarm milk. at this time, egg whites are beaten until stiff-peak forms. Then it's folded into the yolk mixture. dry ingredients (sifted) folded at the end. Goes into the oven (pre-heated/180) until the edges are golden. 

The issue is, at the stage where I add dry ingredients, sometimes I add it in three portions and I sift it over the batter. But some other times I do it at once. I get different textures, soft and fluffy or quite sense. Is adding flour at once causing an undesired texture?
You want the dry ingredients to be fully moistened and dispersed throughout the liquid with no dry clumps.  You also want minimal agitation so that you don't destroy the retrained air, introduced by the whipped egg whites, which acts to give a fluffier texture to the finished cake.

If you sprinkle the dry ingredients over the batter in multiple steps and gently fold in each addition, it requires very little agitation to moisten and incorporate; little more than lightly pressing over the surface with a spatula and a gentle fold or two.

If you add all at once, you have to mix the batter more vigorously to get the dry ingredients to fully incorporate.  This will cause the batter to deflate and will produce a denser cake.