Hi...
I discovered the same thing myself, my name is top around Top 35 at Google for the keyword search phrase:
SEO Expert
I was not even trying to "do this," it just happened naturally, but I can and I will improve the rank (placement) of this keyword phrase for my name.
1. The steps I would take in improve the relevancy would include: Add additional optimized backlinks to other websites, add additional pages to the website with relevant contact, and rewrite some of the content on the current page or pages.
2. It depends on too many "things" to make an accurate prediction, it would most depend on the search engine user, what the person it looking for, and the saturation of relevant results for the term the user is searching for.
3. No, but images can be named and have alternative text assigned to them which can help to optimize them as well.
4. It does not have custom title tags, it does not have anchor text (optimized text links), the Meta tags could be much better, I think it has too many Google Ads, and I think the site could have a better internal link structure with a few more pages. These are just a few things of many that I can see quickly, to better optimize this website you would need to improve on some of the items I noted above.
If you have any further questions, concerns, or comments, please let me know. If you would like to contact me to chat in private, feel free to do so.
Kind Regards,