How Do I Get Images In Masonry and Excerpt Formats

You need to set your featured images: https://generatepress.com/knowledgebase/featured-images/

Let me know if you need more info :)

Can I not have it show the "hero" image on the individual post? What I will end up doing is using one (or the only) image in the post as the "Featured Image"

The blog posts/excerpts use the featured image.

The next version of Page Header also focuses more on using the featured image while keeping the page header image as more of a backup if you need a different image on the single post/page.

I am not sure I am following. Sorry for my confusion.

Here's what my site looks like now with a plugin I have been using:

and what the single post page looks like:

is it possible to recreate this using only GeneratePress?

You should be able to do that exact same thing using featured images in GeneratePress.

Have you tried using featured images yet? Is something about it not working right?

I tried using featured images, but when I do, the featured image shows up at the top of each single post page in giant form.

I suppose that's ok for some posts, but for others (as with this one), I'd really just like that image to be as it is shows up in the body, with a wrap-around of text.

The featured image also doesn't show a caption, so people would have to look at the body of the article for the identical photo to find out what is in the photo.

I looked for a place in the single page template to delete the code that inserts the featured image, but couldn't see anything that was likely.

You can remove it from the single post using the Page Header add-on in "Customize > Layout > Page Header".

Let me know if that helps or not :)