1) Because Salvation is by faith alone does one need to be infant baptized or baptized as an adult in order to go to heaven?
Salvation is by grace alone
through faith alone on account of the righteousness of Christ alone. Faith is the instrument by which a person clings to Christ and His righteousness. God saves unworthy sinners by grace by making them alive (regeneration) and their living hearts turn in reproach of their sin (repentance) and to Christ for refuge (faith). God uses means toward this end - the Word and Sacraments. These are visible, historical means by which God manifests His grace and He works through these means to bring about faith and repentance. Asking whether or not one needs to be baptized is missing the point. God works through Word and Sacrament to convert and save. God does not
need the means to save but Has promised, in His Word, that He uses them for His saving purposes.
2) What does covenant paedo baptism symbolize?
See the Westminster Confession of Faith Chapter 28 (
Westminster Confession of Faith - The PuritanBoard). You can find similar definitions in the major Reformed Confessions. The London Baptist Confession, which you claim to confess, says much the same (minus the covenant of grace part and a few nuances):
"I. Baptism is a sacrament of the New Testament, ordained by Jesus Christ, not only for the solemn admission of the party baptized into the visible Church, but also to be unto him a sign and seal of the covenant of grace, or his ingrafting into Christ, of regeneration, of remission of sins, and of his giving up unto God, through Jesus Christ, to walk in newness of life: which sacrament is, by Christ's own appointment, to be continued in his Churchy until the end of the world."
3) If the child turns out being lets say, extremly anti-christian, what is there relation to the covenant?
Their relation
ship to the Covenant is that of one who shrinks back in disbelief. They are in great danger of falling into the hands of the living God for their highhanded rebellion of the things they have tasted of. Their relationship is one of visible member of the Covenant and the Church needs to make every effort to call them to repentance and faith. Should they continue in their rebellion then they need to be disciplined, expelled from the Church and the visible means of grace, and treated as an unbeliever in the hopes that they might turn and be saved.
4) Where does being regenerated come into this?
God alone is the author and finisher of our faith. The Spirit blows where He Sovereignly determines (John 3). Unless a man be born again he cannot see the Kingdom of God.
Are children somehow regenerated at baptism (I'm guessing a no on the Baptismal Regeneration) or are they saved later on by the grace of God?
See my previous answer. No man knows when the Holy Spirit regenerates and a visible profession cannot make certain to man what is only known by God.