Why do some people naturally get inclination(a quest or sometimes a thirst) on life to know about God? Are they any pious activities that leads to this state in life after life? Please justify with quotes if necessary.
"How come there are nearly 6 billion people but only few attain perfection(self realization)?"
Because only few try/able to opt for it. This is answered in Gita in straight forward way:
BG 7.2-7.3 - I shall tell you in detail of this Knowledge which is combined with realisation (special knowledge), after knowing which there remains nothing else here to be known again. Among several [thousands] of men, a rare one endeavours for perfection. Among [those] perfected ones, rare one knows Me in reality (realisation)
As rightly said in this comment, everyone get "liberation". And few of them attain "self realisation" as quoted in Gita above.
"Why do some people naturally get inclination(a quest or sometimes a thirst) on life to know about Go; Are they any pious activities that leads to this state in life after life?"
That is called Daivi sampadA (divine quality). The opposite is called Asuri sampadA (demonic quality) which are described in Gita chapter 16. Some of those activities which incline towards divnie qualities are:
BG 16.1-16.3 - The Blessed Lord said Fearlessness, purity of mind, persistence in knowledge and yoga, charity and control of the external organs, sacrifice, (scriptural) study, austerity and rectitude; Non-injury, truthfulness, absence of anger, renunciation, control of the internal organ, absence of vilification, kindness to creatures, non-covetousness, gentleness, modesty, freedom from restlessness; Vigour, forgiveness, fortitude, purity, freedom from malice, absence of haughtiness-these, O scion of the Bharata dynasty, are of one born destined to have the divine nature.
I think it's called 'fate' here in the western world, that which governs life on Earth, look at insurance statistics, that doesn't fluctuate much, but are eerily consistent from year to year, even though life should be purely random to science.
In psychological terms it may be due to curiosity, some wants to see what all this historical stuff is about, others 'to know your enemy' to properly counter argue all these religious people.