Guide on adding a new model, animation, and creature to HoMMV

the "stamp" tool

The stamp tool in the game copies one part of the image to another location; it works like a brush. In Photoshop, it's the same, I presume?

the ability to blend layers in various ways (e.g., color, screen, lighten, etc.)

Probably not; at least, I don't understand what you're talking about. There are layers in the game, and you can adjust their transparency. You can, of course, completely change the image within a layer, including brightness, color (either by simply shifting along the spectrum or using the "curves" tool, which changes the color non-linearly), and so on, but as I understand it, you're talking about unusual layer blending functions based on color, and that's not available.

image editing using levels

There is a tool called "levels," like this one, but it might be something else.
Regarding 3D, there's nothing built-in, but... I was surprised to find that there's a plugin. It has a limited number of shapes, according to the description.

Can code also be written in Notepad, theoretically? But is it worth it?

Well, Notepad is like a basic paint program, without the features of the game, but writing something in Notepad++, say, in Python, is quite convenient, and that's what I do.
The reason I work with this program is because I'm a fan of underrated things. Experience shows that often (I don't know if this is the case here, but in general, it often is) people use something out of habit or become victims of hype, and therefore, they don't make the optimal choice. In the case of Photoshop, the non-optimality lies in the fact that it's actually paid software. Yes, Maya is also paid, but it doesn't have any real alternatives in this case, while Photoshop does. That's why the question arises: why is it needed in the first place, and is it really necessary to compromise your conscience or your wallet in this case?
I must say that yes, at least if we're talking about supporting 3D, and if it's actually used when creating textures, then you're probably right... provided that it's done better there.