Hey there! I'm glad you enjoyed reading this article.
With regards to your first question of 'how to estimate the PDF of a stock return '-- I too am embarking on a journey to learn how to do so (whilst adhering to the statistical consequences).
However, from what I've seen they tend to roughly be gaussian (however there are many caveats associated with assuming a gaussian distribution). I will post an article about it soon.
Now answering your second question, yes you are right, the probability distribution was indeed assumed to be a uniform.