Relative to you, the light is travelling at the speed of light away from you. Relative to an observer not travelling at 30m/s, the light travels at the speed of light away from them. I have never really understood this!! I'm sure someone can explain better than me! Haha
No the speed of any electromagnetic wave will not change if you move with it but the frequency will get smaller so it will be slightly shifted towards the blue end of the spectrum