In the iOS app, pulling up a question from the feed gives the standard question view, which provides no means of navigating elsewhere on that site, either to browse or search. This should be changed for feed questions.
For example, I tapped on a highlighted Seasoned Advice question today, and found that I wanted to make a comment pointing to a related question on the site. The best way I could think of finding that post was to leave the app and use my browser. Then I came back with the link to copy-paste in.
Similarly, a question in the feed might be so intriguing that I want to look around for more cool stuff on the site. That requires two taps back and then a search via the "All Sites" menu item.
I'd suggest that questions selected from the feed should get a special header bar (or maybe stuck in between the questions and the answers) that provides a "More posts!" link at least to the site's top view; ideally there would also be a search field that could pop out of it.
Another possibility that would work pretty well, although it's a small tap target on a phone, would be to link the site name that appears under the question title to the site's top view.