Ivy here from Shopify.
For the Google Shopping thumbnail, only the first variant image of a product will be published to Google Shopping, as Google Shopping will directs a customer directly to that product page. There is a third-party app however that claims to allow you to select the second image for Google Shopping, check it out here.
As for changing the image shown for sharing on Social media, this is slightly different. To change this, follow the steps as outlined below:
1 - From your Shopify admin, go to Online Store > Themes.
2 - Click the Customize button besides the theme that you want to edit.
3 - Once you're redirected to the theme editor page, click the "Theme settings" tab.
4 - Click the Social media button.
5 - Under the "Social sharing image" area, click the Select image button and either choose an image to use or upload a new image.
6 - Hit Save.
It can take a few days to weeks for these changes to be reflected but you can attempt to speed up that process by refreshing your information using the Facebook Sharing Debugger tool. Have you done much SEO work on your store? How do you feel things are going at the minute? Is there anything you'd like to improve or change?