You should redirect image URLs during a website migration. Redirect all image URLs to the new URLs of the images. Then check the server logs of your old domain. If there is no crawler activity, you can discard the old domain.

If you are just moving from one domain to the other and the new domain contains the same content and the same URL structure as the old domain then you will not necessarily see a drop of traffic.

In that case, you will see that traffic drops off overtime on one domain and picks up on the other. But overall, you're not losing traffic. It is a fluid transition.

Traffic drops are usually caused by some sort of technical problem. For example, you might have missed half of your re-directions. There can be misconfigurations on the new server, etc.

If you move to a new domain name that was used by a different company before, there might be some issues. In that case, Google might need a little longer to recrawl the website. However, getting a domain that you know is not dealing with issues from the past. Even if it's a domain with a bad history, Google is aware that content on domains does change. Google might not consider it a site move but they might re-crawl and reprocess everything.

Whenever your website has spam problems that Google detects and points them out to you, then you have to fix them. Then it takes a while for Google to understand that it has changed and that everything is better now.

If you buy a domain name that was used for spamming in the past, it can be better to remove the content from the website and wait until Google can see that the spam content has gone.

One plus one will not always equal one when you merge two websites. Combining two sites into one is not the same as a site move to a new domain.

Google has to recrawl all pages when you combine two websites. Depending on how you merge your websites, you might get very different results.

It can take between a day and several weeks until Google has fully recognized the new website. The number of links from other websites also plays a role.

When you move your website to a new domain, there's no special reassessment of your website quality. Google constantly evaluates the quality of your web pages.

If you change the URL structure of your website, Google might take a closer look at the pages. The current state of your web pages is used for the evaluation.

Martin Splitt also listed some ranking signals that Google uses: "How fast is the site? Is this HTTPS or not? Is the content good? What's this page about? [...] There's, like, hundreds of these factors that we look at. And we collect them per page."