I have a Chrome Extension that sends AJAX POST with some data on every page.
The problem is that, Facebook block the AJAX request resulting this:
The only way to perform a cross-origin request when the page's CSP interferes is through a background page. You can find a complete example at Cross-domain XMLHttpRequest using background pages.
Also, is there some place I can use to store data in Chrome Extension while using content scripts?
Use the chrome.storage API, or use message passing and localStorage
. See this answer for a more detailed explanation and sample code.