No. The browser will send the same information on a refresh as if the user had just come to that page, with the same referrer information. Hence the problem of double-POSTing if someone refreshes the destination page for a form.
What you could do is have a refresh button on the page (as Google Ads used to have before they removed it), which you could use to ...
Browsers do send additional headers, but behavior different. This info in link a bit outdated: stackoverflow question
Looks like Cache-control:no-cache is the best solution, to check for Ctrl+F5, but better to check not the only one header.
Just checked on Firefox Ubuntu, F5 gives nothing, but Ctrl+F5 request contain this
Your screen shot has nothing to do with "cache from image short lifetime".
The warning from google is about HTTPS.
You should get an SSL certificate, which can be free or paid, from your hosting or third party.
When it comes to "cache from image short lifetime", what you could do, in case you have access to .htaccess file (usually placed in root directory) ...