@yanabg
The problem is that using the Yoast plugin the image that I put for Google results is displayed as the first in the page itself. That should not be the case. I should be able to put a picture for Google without having to be in the content of the page itself.
The image that you uploaded as a Featured image for that post from the admin would show on the content of the page because it is controlled by your theme. You might contact your theme developer to remove this feature for you.
If I don’t put any picture, the first picture from the page is displayed and I don’t think that’s right, I should be able to choose a different picture for google results. Right?
The image in the snippet preview (for mobile) was introduced in v12.4 of the Yoast SEO for WordPress plugin. You can learn more about it here — https://yoast.com/yoast-seo-12-4/
For some search results on mobile, Google will now show the main image next to it. In Yoast SEO 12.4, we automatically use your featured image to mimic the way Google does this now. We’ll use the first image in your content if you haven’t set a featured image. Remember, this only works in the mobile snippet preview.
We would first recommend checking to ensure that the image that is appearing in the snippet preview for that URL meets Google’s guidelines here: https://developers.google.com/search/docs/data-types/article#article-types.
We output that image into the source code with instructions that tell Google to use that image. If the image does not meet Google’s guidelines, Google may decide to not use it. In this manner, we suggest examining the image and confirming it does.