Thanks for the replies.
I have managed to go a little further, but not so further to fix all the fiber tear-up issues I had.
Some tips you gave me help the improvement on my planing skills, and reassured me that is not only me, but somehow it is “normal”.
Skew the plane, reduce plane “speed” and plane diagonal/transverse the fiber really help in some spots. Regarding the grade of the boards, I do not konw how to asses them . I have uploaded a picture of the boards I am using. I had some cherry logs, and made boards out of them at a local millsaw. Then I have dried the boards at home.
Maybe some issues started here, with distorsions, cracks, maybe wood not enough dry to be worked (9 months drying, no moisture meter).
I work under a shed, open on 2 sides, and air moisture level change a lot with the weather. Can rainy days add some more difficulties regarding tear-up?