Let's circle back to this. You're not universalist (all saved regardless of faith in Christ). What's the other term for requiring mental ascent to salvation (adult baptism)? Is that your view, say regards #3?
GCC addressed this question very well in the post below.
Saving faith is not the same as belief. Saving faith is the trust and dependence that characterizes a person who is in a state of grace, and that grace is given in baptism just as surely as it is given through the preached word.
Belief is important because it is the conscious expression of existential faith. Just as faith is trust in and dependence upon grace, so too belief is not merely knowledge and assent but also belief that clings to the promises of God- not just that Christ died, but that Christ died for me; not just that Christ is risen, but that Christ is risen for our salvation. It's what distinguishes the belief of demons from the faith of Christians.
But that sort of belief is only the conscious expression of a deeper reality that is only true when God makes it true: that he has handed over his inheritance to us. And he does that in Holy Baptism.
So we have faith (trust) in Christ, saving faith, given as a gift by God through his Word, both proclaimed and sacramental according to the promises of God revealed in Scripture. Since this faith is a gift given by God it requires no preconditions, no abilities of the recipient, no conscious mental assent.
This Christian faith is analogous to the inheritance, name, familial membership, love, protection, and provision received and promised when a child is born naturally into a family. This is the reason that Christ and the Apostles repeatedly refer to regeneration in Christ as new birth.
The mental assent you refer to above is therefore secondary, a product of saving faith given by God. It is an act of the believer done in faith, a work of faith as spoken of in 1 Thess 1:3. It is a characteristic of one who has been granted saving faith in Christ by God, yet it is not possible before and until God has acted to justify the individual, as seen in 1 Cor 12:3.
The Church (rightly or wrongly) has always required catechesis of new adult and adolescent converts before Baptism. There is a desire to see evidence of the gift of saving faith before one is accepted into the fellowship of believers. It is not a denial of the efficacy of Holy Baptism that produced this practice, but probably fear of infiltration and persecution. These people are initially granted faith in Christ by God through hearing the proclamation of the Gospel, yet when they are baptized, all the promises of God made to the baptized are no less valid for them.
There is also a desire on the part of the individual, once they are cognizant of their person, place and situation, to have an understanding of the rite they are submitting to. In other words, you can't really effectively evangelize by forcing people to be baptized, as has indeed been practiced in some historical instances.
But for infants and small children of believers and new converts, the promises of God given in Scripture tell us that God acts to grant saving faith in Holy Baptism. They are baptized, and then taught later as Christ commanded the Church to do. For them, the gift of faith in Christ is given first in Holy Baptism and then as their mind develops they are catechized at an age appropriate level. This is practiced because there are no age limits given in Scripture for those who may be baptized, and because the saving work of God requires no preconditions or participation from the one being saved.