So to get back to you original questions:
So I want to know: 1. What is a "window brush?" 2. What are the "window channels?" 3. What id the "adhesive pad?" 4. Should any/all of these things be necessary to replace, when I replace the windshield?
1 - the "window brush" is the fuzzy bit that runs along the inside and outside bottom of the door windows. It is there to try to make the bottom of the window somewhat air tight. There is a similar brush along the sides of the sunroof if you have one.
2 - the "window channel" is a U shaped channel that fits along the sides and top of the door windows (the ones that open) - the windows slide up and down through the window channel.
3 - I'm not sure about the "adhesive pad" but I suspect it holds the bottom of the door windows.
4 - the windshield and the read window are held in place by rubber seals and they dry out and need to be replaced. The door windows have the window brush and the window channel these also age and need to be replaced but they are different jobs and do not need to be done at the same time.
Your windshield and rear window will leak when they get old and this can be a big problem as the water will dribble down under the carpet (where you might not even notice) but rust never sleeps… need I say more?
The windows on your doors have always leaked since they can move up and down and they will simply allow any water that enters the door to leak out through the bottom of the door to outside the car (so no problem). But you still want to replace the brush and channel because if they are worn leaves and twigs can get into your door and block up the holes in the bottom and more importantly the wind noise while your driving at high speed will be worse with worn ones.
If you do redo the doors you should also rebuild and lubricate the window regulators (the series of leavers and gears that move the window up and down). A used window regulator can cost you $300 but the rebuild kist are $15.