How do I rearrange photos in the Photo app on my iMac?

If you are using the provided "Favorites" view (not an Album) then, like I had said, you cannot change the order. In any view, you can see the options in the menu View>Sort.

For your scans, your options are:

1. In Favorites, select all, and then use the menu "File>New Album with Selection" to create your own album. Then you can arrange them in a custom order. Or…
2. Change the dates on these pictures with the Menu "Image>Adjust Date and Time..." to get these scans in the right places. This works in all views, but it is a bit tedious.
3. In your own album, you can put the date, like 1932 07 04 at the start of titles, and then sort by title.

I'd pick #1, get them in order, and then fix the dates at my leisure.

As Yer_Man said, If your pictures are in Albums, then you can drag pictures around anyway you like, or you can use the menu View>Sort.

In most views other than Albums, like Duplicates or Trips, the order is set by the criteria of that view. The one "provided" view that you can change is Library-- in View>Sort.

By the way, Apple has made an iPhoto app (which was discontinued 10 years ago) and a Photos app. So when you refer to "the Photo app" we can get confused, since there is no app named Photo. We're guessing you mean the current app, Photos.

This is such a vague question... what's wrong with how they are arranged now? How do you want them arranged? You can make albums and drag images into your preferred arrangement in those.

Cool!

Also, if they were scanned they might not have the correct dates, instead they have the date they were scanned. You can change the date in iMovie.