A better perspective is to acknowledge that a saved person will pray. A person who has been given faith in Jesus Christ as Lord and Savior wants to obey God and be closer to Him, whereas the reprobate does not.
A renewed mind prays. Thus, such a person learns of God to some degree.
Scripture tells us it's the Holy Spirit who renews our mind. If the Holy Spirit renews a man's mind, then does the Holy Spirit renew some men's minds more than other men's minds?
Such language is strange to me, because my definition of "saved" refers to final salvation in heaven. I have already given you 2 Peter 2 and his take on it being better to never have been 'saved' in the first place if it means learning about Christ and subsequently falling away. Jesus tells a similar story regarding the one demon cast out, and then returning with seven more demons...
Your idea of 'being saved' is not the same as final salvation. As such, your definition doesn't make sense to me.
Scripture tells us it's the Holy Spirit who renews our mind. If the Holy Spirit renews a man's mind, then does the Holy Spirit renew some men's minds more than other men's minds? Again, I have already offered you Scriptures that can be understood that the Spirit can and does "gift" some more than others. For example, the parable of the talents, you will note that some have received more. God gives ALL of us particular and unequal shares of Himself. All of them separately are sufficient for us. God does not "short-change" ANYONE so that they cannot later say "God, you didn't give me enough graces". As you have already admitted, God gives ALL men sufficient graces. They become "effective" as a result of the fruit that results. How much the "soil" matters in the production of this fruit is beyond me. But it is certainly Scriptural to expect men to respond to God - and those who do not are in trouble of facing eternity without God.
Regards