Lists, Local, and Federated Timelines
You can switch between various lists from your Home timeline. Just tap on the Home title button at the top and you can select from one of your lists, the Federated timeline, or your local instance timeline.
Search and Filters
The search icon in the top right corner for timeline views is for searching through the loaded posts. It cannot find results that are not already loaded in the timeline. You can also create and save powerful filters (basically saved searches) from the filter icon, or choose one of the quick filters to the right of it.