Using "red shift" and "Doppler effect" interchangably is a common mistake. While it is true that a Doppler effect is measurable for stars in our galaxy and for nearby galaxies (the shift can be "red" or "blue"), in most cases, when an astronomer refers to "red shift" they mean the stretching of photons by the expansion of the universe. To quote your first source,
"...all distant galaxies show a red shift proportional to their distance from the earth as a result of the general expansion of the universe (see Hubble's law)..."
In other words, the Doppler effect is an example of red shift, but not all red shifts are caused by the Doppler effect.
But this is getting off topic.
Quote:
If light is being emitted from a source at 3x10^8m/s and I travel away from that source at 1x10^8m/s, then the light will approach me at 3x10^8m/s - 1x10^8m/s = 2x10^8m/s.
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Wrong.
"The speed of light is the same for all observers, no matter what their relative speeds."