You could use a USB OTG adapter to plug a USB Flash Drive into your phone. Few if any apps would move from internal storage. Apps would need to be specifically coded by their developer to allow a move to external storage. Not many app developers bother to so code their apps. This might be marginally useful for adding storage for photos, music or videos.
You do not need a USB OTG adapter to connect your Moto X1 to your computer for the purpose of moving pictures from your phone to a computer. A standard USB to Micro USB charge and sync cable such as the one that came with your Moto X1 allows for that.
No, the Moto X1 doesn’t allow for expanding memory via MicroSD card.
Please see here: Moto E: Make the most of your phone's available storage. Though written for a different phone, the linked section of the article applies to a Moto X1 also.