I want to ask someone what they heard about my country; whether it's positive things or negative things.
Can I say "What image do you have about my country?"
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To me the word "image" sounds unusual here, especially coupled with "about".
I think a more common way to ask this question would be "What impression do you have about my country?"
The meaning here of "impression" is
an idea, feeling, or opinion about something or someone, especially one formed without conscious thought or on the basis of little evidence. (Oxford Languages)
We have an image (a mental picture) of something, not about it.
A chart from Google Ngram comparing the instances of image of (blue line), and image about (red line)
The corpus from english-corpora.org/coca/ contains a few instances of "image about".
Sadly the website really dislikes hotlinking, so any users who would like to personally repeat the results I have found will need to perform a (free) registration and enter the query themselves.
But here are a few examples: