There is at least one tutorial on the EXT site that explains how to use EXT widgets with PHP. There are actually several examples, including at least one EXT sample from Jack Slocum that shows how to use an RSS proxy to build a newsfeeds component. You may find more or articles on the web if you do some searches (many developers post their solutions on blogs). EXT features adapters like YUI, allowing various AJAX libraries to be used in conjunction with EXT.
EXT is a large library, and depending on the number of widgets used, can slow down a CI application considerably, but it is possible to build a custom version of EXT that only uses a select set of widgets and their library dependencies. I would not recommend using EXT for the frontend of a site (consider something like JQuery for the frontend) unless a small set of widgets are used, but the reduction in throughput might be acceptable for an Admin application where you might want to handle drag and drop operations (e.g, drags from a tree to list or datagrid or vice versa). The EXT Layout library in conjunction with CI views makes a nice solution for Admin dashboards or complex Web 2.0 solutions (e.g., an interface similar to a desktop application).
I plan to release a sample application later with a EventListener library, based on the Observer pattern. It’s based on using EXT and JQuery with CI. It allows a CI controller to trigger events. This is still in the experimental stage, but it might allow CI to also work with the components from a framework like PRADO without using their application wrapper.