Starling includes a sample which you can look at to get an idea of what its capable of. The demo is included with the source and a Flash version you can play is here – click on Start Starling Demo.
As for your particular queries yes it can do all of those. Changing resolution and resizing content are easy to do, though you have to hook it into your own code in a way that makes sense – do you just want to scale everything or reflow content for example? Dynamic geometry is certainly possible, you can manipulate vertices directly to achieve a variety of dynamic effects. And shaders are fully supported, though you need to work at a low level to work with them. There is no high level shader language, just AGAL.