There's something I'd like to understand. Is UTC the same as GMT? While growing up, I heard majorly about GMT, but it seems UTC has overridden that.

There is a slight difference, at the conceptual level: UTC is a time standard and GMT is a time zone. But the time itself is the same.

An unrelated question: I read an article that stated that the earth's day is getting longer by few miliseconds every 100years. Does this have effect on the Gravitational time dilation?

Every thousands of years actually. In principle, there is an impact, but you need to integrated over billions of years to notice it.