I was roaming on my terrace and I saw star-like moving object that gradually became small, red colour and disappear. Within a few minutes I saw another similar-looking object a little distance away coming from opposite of first one and disappearing with red colour at nearly the same location. Within 5-6 minutes, I saw another similar object that soon disappeared. The object was moving from a lower altitude to a higher one. What was it?
You may have seen some artificial satellites passing into the Earth's shadow. If so, Heavens-Above could help you identify them. The reddish color just before disappearance would be due to the atmosphere scattering shorter wavelengths of sunlight.
That can be Draconids meteor shower. It's peak date was 8 October.
So, there are quite great chances that you saw some of the meteors from Draconids.
Also, meteors from showers can appear from anywhere, and go anywhere: they can go from high to low altitudes or even low to high.
You also mentioned about color. As the meteors enter the atmosphere and burn up, according to the temperature they can produce different colors.