So which way would be more common in spoken language? 아이가 or 아이들이...... It seems that the plural marker is optional.

I translated it as "happy" and it's still correct. So what is the diffrence between "기쁘다" and "행복하다"? As far as I know, "행복" is a hanja (chinese-root word) which means happy. Am I right that "끼쁘다" is the pure korean word that has the same meaning?

I think 기쁩니다 should means happy. Well, glad are usable too but it didn't match with the sentence meaning. Glad more to a 다행이다.