You don’t necessarily need your own motor and driver if you can find a cheap motorise-your-blinds-kit and just fiddle its controls (e.g. with the relay shield or your own transistor circuitry 
).
With non-Particle dedicated shields that have a high current demand (like a motor shield) it’s usually necessary to power the shield and the Particle seperately. If yhe shield has a 5V or 3.3V output, you can power the Particle off that but need to make sure it’s properly filtered DC.
Running off a battery will be tricky since the motors do need some power.
About IR there are some threads here discussing that, and the a good place to look is at AnalysIR