Sorry for the inconvenience caused. Here is the explanation of all your answer:
Do I need to reinstall the Pure and Simple theme in order to get the Pro version in WordPress?
Yes you have download the puresimple pro from our site and upload to your website. Go to pro section on customizer is a just a link to pro version of theme.
how do I change the banner image?
When you upgrade to pro version you will not get those default content.
Please do visit to free theme support forum for free theme query.
In pro version you can keep banner image by dragging text widgets on to the banner sidebar . Then you can place html snippet for image tag. <img src="url of the image" />
Let us know if you have any question or queries regarding to this.