The answer to this question might have changed since it was first asked nine years ago: very soon, a book will be available whose goal it is to give a detailed elaboration on Freedman's work:

[*The Disc Embedding Theorem*](https://global.oup.com/academic/product/the-disc-embedding-theorem-9780198841319?cc=de&lang=en&), ed. Behrens, Kalmar, Kim, Powell, Ray. Oxford University Press, to appear July 2021.