The easiest way in both would be to integrate the browser in the web app but perhaps restrict it to the blog.
For example, your app would open and have its own UI, but displaying the actual blog content would be done in an integrated browser (such as a WebView in Android).
Doing it this way isn't the best as it wouldn't be the best experience for the user, but it has the added benefit of keeping all the blog's design and extras, as well as javascript functionality.
"Manipulating incoming data from the website" (otherwise known as scraping) would be tricky for modern blogs since they usually contain so much customised content and are nowadays more like websites with blogs than just regular blogs.