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R1 is causing a voltage drop in the output signal. The more current that the transistor pulls, the more voltage drop you will see over R1 and the lower the output voltage will appear. Unfortunately, I don't know exactly what is typically done, but that setup seems like it will always have that...
I believe that the noise is just essentially thermal noise for resistances, transistor noise, and other intrinsic noises that occur in your circuit. This isn't noise being "added," it is just noise being recognized.
This is a terrible explanation probably, but if I understand your question clearly, then the concept of routing metal layers in only one orientation per layer comes from digital design. This concept I believe stems from the use of APR (Auto-Place & Route) tools, ease of layout, and prevention...
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