texture lookup
I’m not 100% certain, but as far as I heard of it, this is the process of loading a texture into the graphicscard memory (GDDR). UV are usually texture coordiantes (x,y->u,v) ranging from 0 to 1. You might see UVW for volumetric textures. So if you have a texture streched across your whole screen you’d just need to multiply the UV coordinate with your screen resolution the get the pixelposition. But most Textures are distorted by perspective on a 3d object.
Color
R = red, G = green, B = blue, A= alpha. Textures from the render process just have alpha on 1, wich means fully opaque. I never used it, but I guess it’s useful for compositing, like Slate/UMG (User Interface stuff).
Size/InvSize
Yes, just the Pixel resolution. By the way: epic staff also programmed debug nodes to see these values rendered as numbers. Just search for debug when you add a node. These only work for pixel position independent values. If you would e.g. set the pixel colors as input, you would just see fragmentations of numbers.
in the screenshot it displays the preview window resolution.
Tonemapper
This is specific to postprocessing materials. The tonemapper includes the exposure process. You can set the postprocess to happen before the tonemapper, after or you can replace it with your own function. If I’m not mistaking: If you set it before Tonemapper you get a higher range of color (16bit per channel?) to work with, instead of the usually mapped and cut of 8bit colors for standard monitors. I don’t know how this is implemented with HDR monitors.