Does my success in the competition – with the help of my friend despite my lack of documentation, and the inability of others with the same lack to participate – count as taking someone else's place?

There is no harm in remaining in the job as long as the field of work is permissible, and you believe or are certain that you are more deserving of it than others, especially since you do not know the reason for obtaining it, whether it was through assistance or due to your good performance.