Everybody in the beginning has trouble with notes being too loud on fingers 1,2, and too soft on fingers 4,5. If one has the patience, one can start on exercises right at the beginning, aiming at playing all the notes at the same volume. I learned evenness starting age 8 on Schmitt exercises, that are available for download from Pianostreet. I did ten minutes of these exercises a day the first year. In fact the goal of my starting piano was to train me to use my third finger RH that the fingertip had been cut off. So evenness of finger strength (or use) was the primary goal of my piano lesson.
But many teachers are afraid of discouraging the student with too much boring drill, and won't give young students these exercises. After all if the student quits, the teacher doesn't get paid. But there is no substitute for practice, and these boring exercises give it to you. I recently stumbled on a Hanon first book (as selected by Schaum) and these exercises seemed to be similar to the Schmitt. I'm not familiar with the german language exercise book you have selected, I hope it is similar and as good as schmitt in creating evenness and flexibility.
As far as accenting the first beat always, last year at my first piano lesson in 51 years, the teacher insisted I play the first movement of Moonlight Sonata with the first beat of every measure accented. I did it her way during the lesson, but I think that makes Moonlight sound like the lovers are riding a Swiss lake steamboat in a crowd at 2 PM, instead of sculling across Lake Como in the dark in a small boat alone together. Sculling is a motion where the movements are very even. I'll never play Moonlight with the first beat accented again.
Playing to win competitions, and making art in music, are different tasks, IMHO. Accenting the first beat always is imperative in military band marches, where that cue is part of getting the soldiers to march together. Not all art is a military march.