During my 40+ years as a Christian (which was marked at the start by full water immersion, as a believing adult) I came to learn much about those who practice paedobaptism, and why they do that. One book written by a Reformed theologian had a chapter on Christian Baptism, parts of which might give the answers you seek. At the start, he makes these points, which are worth bearing in mind:
"I don't regard this debate between Baptists and Paedobaptists as a
debate about fundamentals... The divergence itself is not one between
Christians and non-Christians. It is very much an in-house division,
dividing for example, men such as C.H. Spurgeon and John Kennedy, who
on all fundamentals were agreed... those of us who adhere to the
doctrine of infant baptism are not necessarily sacramentalists. We do
not believe that baptism, by itself, mechanically and invariably
effects a saving change in children. We certainly do not administer it
in the belief that it automatically regenerates." (A Faith To Live
By, p210, Donald Macleod, Christian Focus, Mentor)
As twelve pages are taken to go into reasons for paedobaptism, I shall only select bits that have a bearing on those scripture texts cited in the Westminster Confession of Faith. Only six of those texts are addressed, so I shall confine my quotes to parts dealing with them (though not in that order; they will be highlighted in bold.) It also needs to be said that many other texts are used in the book to support paedobaptism. As I am not answering so as to promote one stance or the other, I shall just try to present in a fair manner what this book says, in its own page order, regarding those six texts.
"Who ought to be baptised? ...Those who are believers! That point
needs no demonstration. It is plan enough in the New Testament that
adults were baptised on profession of faith. But the Reformed
Confessions have gone beyond that and said that we should also baptise
'the infants of one or both believing parents'.
The question is, Do believing parents have the right to have their
faith in Christ registered in an act of baptism which includes not
only themselves but their families?... the traditional argument of
Presbyterians on this issue is still valid. That argument revolves
around the fact that when God established His covenant with Abraham He
stipulated that the sign of the spiritual covenant should be
administered to the physical seed...
In fact, the terms of the Abrahamic covenant make it plain that it was
understood by Abraham himself in spiritual terms. The core promise was
that God would be his God and the God of his seed (Genesis
17:4ff.) Circumcision was the sign of that promise. This is how
Abraham himself understood it; it made him look for a 'city with
foundations, whose architect and builder is God' (Heb.11:10).
This is confirmed when we read in Galatians 3:14 that we ourselves
as Christians are the beneficiaries of this very same Abrahamic
covenant. We are the ones who have experienced the real fruition of
its terms and promises. 'Christ,' says St. Paul, 'redeemed us from the
curse of the law by becoming a curse for us' (Galatians 3:13).
Why? 'That the blessing given to Abraham might come to the Gentiles
through Christ Jesus.' And what was that blessing? 'That by faith we
might receive the promise of the Spirit.'
The Abrahamic covenant was undeniably spiritual. It was God's
irrevocable commitment to Abraham and to his seed. It was the promise
of an eternal city of God. It was the promise of redemption from the
curse of sin. It was the promise of the Spirit. And when the apostles
saw the New Testament inheritance unfolding before their eyes they
said, 'This is what God promised Abraham!' Indeed, when Jesus said,
'Go and make disciples of all nations' (Matthew 28:19), he was
echoing God's promise to Abraham, 'Through your offspring all nations
on earth will be blessed' (Genesis 22:18). The church is sent
precisely to bring to all nations the blessing God promised them in
Abraham. Yet although it was so clearly a spiritual covenant, the sign
was to be administered to the physical seed... on all those born
within the family of Israel. That is why not only Jacob but also Esau
was circumcised. It is not the elect who receive the sign. It is not
the born-again who receive the sign. It is the physical seed... Esau
stands there reminding us that not all the physical seed are elect or
born again or saved...
It is a remarkable thing that when Christ came He did not institute a
new church, but simply grafted the Gentiles on to the old Abrahamic
stock. We are the new Israel. We are the Israel of God. We are the
seed of Abraham. We are the wild branches grafted into the original
olive tree (Romans 11:17ff.) It is a magnificent symbol! God did not
plant a separate New Testament church or a separate Gentile church.
That is why, when the gospel came to the Samaritans they were not
brought to perfection until the apostles came from Jerusalem, and
then, in fellowship with the church in Jerusalem, they received
baptism in the Spirit (Acts 8 : 14-17).
If, then, it is the same covenant and the same church it seems
reasonable to assume that the comforting provision that God made -
that when a man comes to faith he may embrace his children with
himself under the sign of the covenant - would remain in place. This
is precisely what we find... The passages commonly adduced as
arguments for infant baptism (e.g. Matthew 19:14, Mark 10:14, Luke
18:16, 1 Corinthians 7:14) merely confirm this. The children of
believers continue to have the same special relationship to the
covenant as their Old Testament counterparts had; and, consequently,
the same right to the covenant sign.
Why do I baptise children? ...It is because God gave me an ordinance:
Put the sign of the spiritual covenant on the physical seed." (Ibid.
pp 215 - 219)
Now, the entire chapter in this book needs to be read, to do justice to the argument for baptising infants. I have confined myself to your question, and to some of the texts you ask about. I have my own questions about only male children being circumcised, yet male and females can be water-baptised; indeed, I feel a question coming on!
However, this may go some way to showing a Reformed minister's explanation, a man who stoutly agrees with the Westminster Confession of Faith, and who uses some of those texts in his chapter on the subject. I make no judgment here on whether that Westminster Confession is faithful to the scriptures it cites. I simply present a few examples of how they are applied.
