How do I know that the disavowed links I just uploaded have reached Google? Will I get an email notification? How long will I have to wait to see the result?
Google will take the disavowed links into account when they crawl them again. Unfortunately they will not provide you with a confirmation mail or email notification (They only give you a confirmation that you have uploaded the disavow file successfully). So it depends when your site will get crawled again.
However we strongly recommend you to use the advanced tool Link Detox Boost to speed up the process of Google factoring in your disavow file.