So what you're saying is that I can't use wordpress for any Etsy or Amazon links at all. This doesn't make sense.
No it doesn't (and timethief isn't WP staff). Of course you can link to your Etsy shop, or to an Amazon page for a book you've written (or to an Amazon page for a book that's written by someone else). You only violate the ToS if your blog is designed exclusively or primarily for driving traffic to other sites, or if it includes links to pay-per-click schemes etc, or if it includes ads you get paid for, and so on.
To remove the phone image, go to Appearance > Widgets, open the Image widget you'll see in the Sidebar section, click Delete.
To create an image link, you copy the image to your computer, upload it to your blog via Media > Add New, click Edit once it's uploaded, and copy its address from the "File URL" field of the Save module; then you go to Appearance > Widgets, drag an Image widget to Sidebar, paste the image address in the "Image URL" field, paste the webpage address in the "Link URL" field, save.