By this, I mean if I wanted only the classes of forge that preload a texture index, can I have just those files in my mod download, or do people have to externally download and install the whole of forge?

Preloading a texture just tells the renderer to load the texture, its literally a 1 line helper function.

But read the licenses that are included with Forge.

Yes Forge is ©, but it has a very open license.

 

Also, You should use full forge as a base for everything for compatibility sake.

Yeah, as Lex said. It'd be best if you just used Forge to develop your mod overall as it'd be compatible with all the other mods out there that require Forge or ModLoader. (Since forge is backwards compatible with it) Which is the whole point of Forge.

So if I make a mod with the full forge package, then I should get people to install the whole of forge before installing my mod?

Typically how working with a dependancy works.

So if I make a mod with the full forge package, then I should get people to install the whole of forge before installing my mod?

9/10 people will already have it

 

but the main reason for you to use forge is so you can safely create a mod without editing minecraft itself - meaning that all other mods that dont edit minecraft will work with yours without patches!