Will there be an option to ask a question in the Socratic app once the Socratic website is set as "read only" in August?
It's worth pointing out that the changes made to the Socratic website will not affect the Socratic app.
The team designed the app to work independently of the website, as two separate entities. So the fact that the website is transitioning to a read-only version come August 15 will not impact the way you can use the app in any way.
On that note, keep in mind that the questions asked using the app will not make their way to the website. So the answer to your question is 'yes', you will be able to use the app to ask questions after August 15, but these questions will not interact with the website in any way.