No Photos folder/files in Finder?!

There are multiple ways to access your images when they are managed by Photos. None of them include going to the Pictures folder at all.

You can use the share mechanism: that's this icon on the top of the Photos Window

It may have different options depending on how you have yours set up.

Then there's Exporting

File -> Export - and there are a variety of options there, depending one exactly what use you have for the photo. It includes an option to export an unmodified original, as well as edited versions in different sizes and qualities. If I was trying to get prints at Walmart this is what I would use, to ensure the maximum quality.

For uploading to a website like Shutterfly - well first I'd check if they have an extension for Photos that would mean you could use the Share menu, option 1. If not, then in the attach dialogue, look at the left hand panel and note the Media heading:

The contents of your Library will show up in the right. (I've not allowed that on this shot for privacy reasons.)

If you need to access your photos with the Finder you need to export them out of the library to a folder on your Desktop via the File ➙ Export menu, selecting either the edited versions (top selection) or the original unmodified version:

They are stored within the library package.

 Everything I see in Apple says I should have a Media and/or Pictures folder in Finder.

You will see a Pictures folder in the Finder. That's where your Library lives, by default.

The Media heading is not in the Finder, it's in Open... or Attach... dialogues in every app. In your web browser now go command-o and a dialogue will appear asking you which file you want to open. Look at the left hand side of that window for the Media section.

You cannot see the Media Browser in in the Finder. You will see it when you run an application and use the "file > Open" dialog in the application, or the photo browser in the application. The Finder itself does not show the "Media" section in the sidebar.

But not all applications support the Media browser. You need a new and current version, that is fully compatible with your current system version. Which system is installed on your new Mac?

And which application are you running, when you cannot access the Media? Are you accessing WallMart and Shutterfly using a web browser? If yes, which one?

For now I'm just trying to figure out why I cannot access/find my pictures anywhere in Finder. They are not in my Pictures folder, as they should be. 

Actually, they are. They are within the Library Package. That icon you see for Photos Library is actually a special kind of folder, and all your images are stored within it. It has no user-serviceable parts, and mucking around in there can cause damage and dataloss, so it's set up that way.

Your dialogue box has a Media heading - mine does not. It doesn't matter which program I use to open it, there is no Media heading anywhere. 

Does your Dialogue Box have a Sidebar? = that is, a panel on the left with links to various locations, and a different shade from the rest of the window?

You haven't gone crazy. This just happened to me when I upgraded to Catalina, 10.15.1

My Problem: 1. The photo alias in the sidebar doesn't open Photos app. 2. I also can't access photos through a web browser because the link to Photos only goes to the location of Photos, not inside the app.

The default alias 'Photos' in the Finder sidebar takes me to a blank library (yes I have photos in there, circa 2011; legacy problem?).

Example: To upload a photo here, I click on the 'mountain' photo icon below. I have 2 options, Favorites>Pictures, or Media>Photos. 'Pictures' take me to the outer location of photo library. 'Photos' takes me to a blank page.