the equivalent of the q: query feature in the web based version?
Unfortunately, there is no direct search feature in the Android app, but you can perform such query using the "Filter" option.
To do so, please tap on the "Filters" tab in the left pane, at the bottom you'll see "Manage filters", after that - "Add filter". On this screen you will be able to type a name for the new filter and the query. Here, you can use any query just as on the web incl. the q: search.
After that, this filter will be saved and can be easily accessed anytime and also used as the default view for the widget.