My friend (with an account) is unable to see any images on my homebrew creations. I also cannot see them when I am logged out.

This is by design, images on public facing homebrew are disabled

If you can prove you created the image or otherwise own the copyright or have permission to use it on this website, then you can try contacting a moderator to manually approve it. I cannot confirm if they can actually do that but worth a try.

The reason why images were deliberately disabled is partly due to copyright and also so naughty people don't publish with naughty images, since the publishing is automatic and cannot check what images are used.

Understandable, but it's a little annoying that people cannot see the images I created on some of my homebrew. Will people in my campaigns be able to see the images, or would that only work if I don't publish them?

Quote from trapbuilder2 >>

Understandable, but it's a little annoying that people cannot see the images I created on some of my homebrew. Will people in my campaigns be able to see the images, or would that only work if I don't publish them?

 
No Clue, but this can be easily tested. Make or join a campaign and give a link to the unpublished homebrew to another player in the campaign. If they can see the image, it works, if they cannot then it doesn't.