Mostly, yes: GA4 shows it as referral traffic from chatgpt.com. But some AI visits hide as direct traffic, and clicks from Google's own AI Overviews can't be separated at all. How to see what you can, in five minutes.
No, Google doesn't penalize content for being written with AI. Its spam policy targets pages made in bulk with no added value, however they were produced. Here is where the line is, in Google's own words, and what we've seen on our own sites.
Yes, but not the way most people think. Images don't push a page up the normal rankings. Their SEO value is in Google Discover and image search, and only certain kinds help.