How are Buddhist Sacred Texts used in practice and historically, given the questioned authenticity of some of them

From the perspective of authenticity, Pali tipitaka is the most reliable source. Most Mahayana sutras did not come into being until at least 700 years after Buddha's passing.

What is a prescriptions for?

Its main purpose is to cure the ailment of a dis-ease called suffering. Interminable suffering called Samsara.

Over the centuries different traditions have added their own flavours to the original prescriptions to it make it much more appealing and less bitter. The prescriptions still work as can be attested by those who are cured.

The prescriptions nowadays have different sweeteners that all.

Some general guidelines the Buddha gave to Gotami in AN 8.53:

"Gotami, the qualities of which you may know, 'These qualities lead to passion, not to dispassion; to being fettered, not to being unfettered; to accumulating, not to shedding; to self-aggrandizement, not to modesty; to discontent, not to contentment; to entanglement, not to seclusion; to laziness, not to aroused persistence; to being burdensome, not to being unburdensome': You may categorically hold, 'This is not the Dhamma, this is not the Vinaya, this is not the Teacher's instruction.'

"As for the qualities of which you may know, 'These qualities lead to dispassion, not to passion; to being unfettered, not to being fettered; to shedding, not to accumulating; to modesty, not to self-aggrandizement; to contentment, not to discontent; to seclusion, not to entanglement; to aroused persistence, not to laziness; to being unburdensome, not to being burdensome': You may categorically hold, 'This is the Dhamma, this is the Vinaya, this is the Teacher's instruction.'"

Further details to explain those themes are available in AN 8.30

The Tipitaka was written down during the 4th Buddhist council which was held in Sri Lanka. It was headed by Venerable Maharakkhita and five hundred other Arahants. Lord Buddha never said not to accept the word of the Arahanths. Those who question the authenticity of the Tipitaka and the commentaries are just individuals surfacing from time to time. They don't represent any Buddhist council and they might not even have attained any stage of enlightenment. So unless you have undeniable proof that some teaching is not inline with Buddhism, it's best to accept the ruling of the councils instead of accepting the modern commentaries of certain individuals when you don't have proof either way. It takes away the worry of having to prove everything and gives you a nice state of mind to work on your salvation with confidence.

I'm curious on how Buddhist Sacred Texts are used in teachings and in practice [...] what authority do practicing monks and the Sangha give to the sacred texts? How are these texts used? Are they used merely as a guidebook or as intensely analyzed, as say, the Christian Bible?

In general, I think it really depends on the sangha and school. For example, in Sōtō Zen, probably the most read sutra is the Heart Suttra and Dōgen Zengi texts are frequently used. Texts are used by monks in the context of practice and any analysis that sidetracks from this purpose or shows signs of intellectual exercise, even slightly, might be explicitly discouraged (e.g. left to academics).

Monks, in Zen, don't seem very inclined to scholasticism. Also, they don't seem to easily fall in the trap of mixing the value of texts and attachment to it -- as attaching to written words is famously made fun of.

Yet, scholastic work was not only common but prominent in many eras and many traditions. During the early sects, different abhidhamma systems developed and were used as platform for discussing doctrinal points and divergences (even treatises on how to develop formal proofs were elaborated). Also, monks started writing exegesis.

Theravada inherited this tradition. In general, I think its monks, versed not only in the nikayas but in abhidhamma and exegetical literature would not hesitate to scrutinize any doctrinal text and analyze them in their minutia. In many lineages, abhidhamma has a distinguished role, though commentaries often receive surprising authoritative status. For example, some monks see buddhism strictly through the eyes of Buddhagosa.

Another example, Ledi Sayadaw caused great turmoil for writing numerous corrections to a commentarial book -- this reaction certainly smell a little dogmatic and not showing much of the skills of the Buddha's recommendation to the Kalamas. Also, it seems Ledi was a champion in turning abhidhamma as a guide for meditation.

Suttas are also not only restricted to be quoted in dhamma talks. They are chanted, memorized and studied by monks and lay people and they practice meditation following what has been taught in them.

From a more secular perspective the Pail Canon has the definite merit of being closer to the time of the Buddha so could (controversially?) be argued has the greatest authenticity. However there is an enormous canon of Mahayana literature that from a historic point of view was written hundreds of years after the time of the Historical Buddha. To the adherents of these forms of Buddhism these texts most certainly don't lack authenticity. In fact the ones that I'm familiar with go further and insist that they are higher teachings that build on more provisional early texts.

A couple of examples

The Perfection of Wisdom sutras are early Mahayana texts. The tradition goes that the Buddha entrusted the texts to the Nagas (water snakes or dragons). Hundreds of years later Nagarjuna rediscovered these from the nagas then redistributed them to the world. So according to tradition the texts are authentic although they were only available much later on.

Another Mahayana text the Lotus Sutra goes to great lengths to point out that the text is the authentic word of the Buddha even though it was written after his death. It asserts that it is a higher teaching that augments and to some extent supersedes the early texts. In this case the Buddha is still teaching the text but in this work the Buddha is seen more as existing throughout time and takes on a more cosmic aspect so the words been written afterwards become less of a problem. This quote illustrates the timeless aspect of the Buddha in the Lotus sutra

Suppose all these worlds, whether or not a particle was left in them, were reduced to particles, and each particle represented a kalpa. The period of time since I became a buddha would exceed this by hundreds of thousands of myriads of koṭis of nayutas of incalculable kalpas. Since then I have constantly been residing in the sahā world, teaching the Dharma and inspiring sentient beings. I have also been leading and benefiting sentient beings in incalculable hundreds of thousands of myriads of koṭis of nayutas of other worlds.

Use of the texts

As to how people understand of use these texts - since the later texts are still seen as the authentic Buddhist text they will be used in that manner. Bear in mind also there are texts that do not make the claim to be the authentic word of the buddha such as Santideva's Bodhisattvacaryāvatāra. A huge number of people, past and present, find these texts hugely rewarding spiritual works in the same way as people have an enormous regard for Christian works such as An Imitation of Christ. It doesn't need to the the direct word of the the Buddha to be a valuable spiritual work.

I have personally read (a reasonable portion of) the Pali canon and the Mahayana works listed here (Diamond sutra and Heart sutra from the perfection of wisdom) and I would urge anyone who is interested to spend time with the Mahayana texts as well as the Pali Canon texts. It's my belief that these works aren't (just) instructional manuals - the reading of them is an act of devotion and Buddhist practice in and of itself. Read the Lotus Sutra and allow the great swirling cosmic vastness of it all transport you somewhere else.