I have images on the main and the side. On the side, I use scaled-down versions of the main images. Should I remove the scaled-down images from google search results and no index them? If yes, should I no-index them from the robots.txt file?
Image URLs with different resolutions do not present a duplicate content issue. I would not do anything to try to keep your thumbnail images out of the index.
This includes both situations where multiple resolutions are displayed on a page (as in a thumbnail and the main image) and situation where one of the resolutions is displayed (as in
Google may index all of those images, but it will give preference to the highest resolution image. This set up makes sense, given that on their image search application (Google Images) the user has the option to filter based on resolution.
Take for example a Google Image search for 'saturn.' For me, the top result is a 4613x2233 resolution image of the planet Saturn, from wikipedia.
When I select the "Tools" option under the image search bar, and then select the "Size" dropdown and select "Medium". The top result changes to the same image from wikipedia, but in a smaller resolution.
This means the search engine wants to index your different images resolutions, and without any qualifier from the user, will display the highest resolution file.
This is similar to how Google may rank multiple pages of your site for the same keyword, but may sometimes favor one over the other based on its estimation of user intent and how the specific angle of the content on the page matches user intent.
So I would not do anything here.