Interestingly, we can only know that Scripture itself is inspired and infallibly transmitted because of its infallible source: the Church. This article could be helpful, particularly the Spiral Argument paragraph.
Could you give the scripitual citations for the above bold quotes?
Yes. The Church is "the pillar and foundation of truth." Therefore, when the Church teaches something as true, it is true. So when the Church says that the doctrines put forth by a Council are true, they are true. And when the Church teaches that when the Pope speaks ex cathedra he is speaking the truth, he is speaking the truth.
Here's the "spiral argument" that I linked above.
1) Catholics argue that the Bible is the most historically accurate document of the era available to modern man. Some 500 copies exist that are in substantial agreement.
2) These texts include Christ 's prediction that he would build a Church which the gates of hell would not prevail against, and which is "the pillar and foundation of truth." The Scriptures also show apostolic succession in Acts.
3) History shows that the Catholic Church has existed since Pentacost with an unbroken line of apostolic and papal succession.
4) The existence of this organization, with unbroken apostolic and papal succession, unparalleled in human history, is extremely strong evidence for divine protection.
5) This divinely protected Church tells us that the Bible is inspired, determines the canon of Scripture, and preserved Scripture inerrantly.
6) Therefore we can know with moral certainty that the Bible Catholics have today contains the books of the Bible that are inspired, and that the Scriptures have not been corrupted.