Offline mode
Again, I fail to see the usefulness of such a feature for a discussion forum. What I see is a bunch of complexity: software architecture changes, synchronizing changes (or things like read state), etc. Some of that might be nice to some, but given the returns for such a large cost, it is not very high on my list of priorities at the moment.
App mode
While I understand that it might seem nice to have Flarum open in a standalone app shell, I'd again ask you to consider the complexities involved: Having no browser window means there is no back button (hello iOS), which means that every single page of the application needs to offer a way to get back to the previous screen - otherwise the user might get stuck, which is horrible. It gets even more complex when users open other websites through links in the Flarum forum.
With that said, I have nothing against adding an app manifest and taking care of other preconditions, so that we can benefit from app install banners. But apart from that, I think smartphone users should get used to opening websites from their start screen that open in a normal browser window.
