Hi,
Well, for the delete buttons, you could not display them by turning off the corresponding setting of the cart module. You could also use CSS to reduce the width of the other columns. Also, if your prices don't need decimals, you could edit your currency in the menu System>Currencies and set the number of decimals to 0. That will reduce the width needed for the prices.
For the captcha, I would recommend activated the invisible mode in the settings of the plugin. That way, it wouldn't appear on the checkout registration form. It will be easier than trying to adapt the width of the area, as this comes from Recaptcha directly, not the plugin we provide.
Regarding the badges, well that's a complex matter. Normally, HikaShop fixes the width of the images on the listings. That way, regardless of the width available, the badges will display the same compared to the images. However, it seems that your listing is customized to allow for two columns instead of one, and that you have custom CSS to reduce the width of the image dynamically based on the available space. That's ok but if you use badges, then you're screwed because the positionning and size of the badge can't adapt to the size and position of the image. And that's why we don't do the modifications you've made to your listing.
You can cope with that using custom CSS to adapt the size and position of the badge using the @media CSS mechanism.