Additionally I'm having a hard time answering the question of how clergy would determine how much time you'd get off of purgatory.

So, this is a topic that requires a couple of mental shifts from the modern perspective in order to understand where medieval people were coming from.

First is the question of "quantitative religion"--that is, measuring God's grace, forgiveness, and sin in numerical amounts. We have the remnants of this tradition today; how often do we joke about selling one's soul? (As far as I've been able to track, this concept arises out of the medieval Theophilus tradition, a precursor to Faustus, whose early examples involve Theophilus exchanging his soul for a legal charter but use financial terms in later versions of the legend).

In the fifteenth century (to scholars, either 1380 or 1418 to 1520, just roll with it :D ), though, this numerical piety was ALL the rage. Medieval scholars in universities had spent the previous couple of centuries bringing order to nature and theology through categorizing everything, explaining everything, proving everything. This has sometimes been called a proto-scientific or prescientific mindset. Medieval people haven't developed the idea of experimenting and scientific observation, but they increasingly need concrete evidence and proof for things like whether praying for the souls of dead relatives are effective.

A good example of this shift is mystical visions from God (like in the Book of Revelation). In the twelfth century, medieval people were pretty accepting of the idea that God would send revelations to a particular person based on things like their ability to communicate the revelations in writing or the support of other people (especially clerics). From the thirteenth century into the fourteenth, at the same time scholars like Thomas Aquinas are working on philosophically proving things like the existence of God, medieval saints have to prove their visions are real through physical exercises like depriving themselves of worldly comforts. By the fifteenth century, the default belief is that visions are false, but saints can still prove theirs are different and genuine through methods like having prophecies be fulfilled or really excessive deprivation of things like food. (Around 1410, for example, Elsbeth Achler was said not to have eaten anything for three years. Meanwhile, the other nuns in her convent complained that food was disappearing from the kitchen.)

So fifteenth-century people want things they can wrap their minds around, see with their eyes, to ground the things they can't (the infiniteness of God, God's interaction with humans, salvation). Especially in new cities, where keeping records of costs and profits and wages are crucial to people's lives on Earth, numbers of costs and profits provide a tangible way to think about people's lives after Earth.

Well, sort of, and this is part 2.

The "popular math of purgatory" does not make numerical sense. It just doesn't. If you have two copies of an otherwise identical prayer book, one book's owner might have scribbled in the margins "10 years off purgatory for saying this prayer" and another person's might say "1000 years off purgatory." I study one text that talks about "losing 3 weeks of grace" and "having more grace than a nun who has spent 30 years in a convent." Basically, the fact that there were numbers as something to think about concretely was what mattered, not what we would consider the actual arithmetic of it all.

Did the clergy of the Middle Ages through the period of the Protestant Reformation actually believe in indulgences? Or did Catholic clergy knowingly deceive people to pocket the money for their lifestyles and building projects?

The disclaimer here is that it is impossible to say what anyone "really believed." All we have is writing. (ETA: We have an amazing amount of non-textual evidence, such as statues and images that we know people used as aids in prayer, and of course churches packed with gorgeous art used to teach as well as overwhelm--but as far as people's words go, we have things written for an audience, not internal thoughts).

And for the fifteenth century, although nearly all written output is religious (something like 80% of texts in 15C Germany), most of it is very standardized prayer texts and books meant to teach the basics of Christianity to lay people and a little beyond the basics to clergy. But just like with the practice of counting years in/off purgatory, considering the wider historical context of the Middle Ages can help answer this question. :)

The Fourth Lateran Council in 1215 is usually seen as a watershed moment in Church history: it's when the Church formally mobilizes to actively work for the salvation of Christian laity at all levels of society. Obviously this doesn't happen overnight. (You can even find some older scholarship that argues Europe wasn't Christianized until after the Reformation, but current scholars would mostly disagree). This means that the Church as an institution, including its clergy, are very important as infrastructure. And, it it apparent, the tangibility of splendid churches was on one hand a crucial teaching tool (art is the "book of the illiterate," as a famous early medieval pope put it); on the other, it was the type of 'proof' or demonstration of God's power.

Now, the lavish lifestyles of a small proportion of clergy, especially in the mendicant orders (Franciscans and Dominicans)--that was a question fiercely debated from the beginnings of those orders around 1215. (That date is not a coincidence: the Fs and Ds were the main "preaching orders" of the Middle Ages; the friars' job was to teach and preach to lay people especially in cities). Franciscan and Dominican authors insist that supporting the spiritually poor (themselves) is crucial to the work of God. Clergy who are not members of those orders, along with lay people like William Langland, the author of Piers Plowman, sometimes have a different view. :P

The lesson there is that "the clergy" of the late medieval Church are by no means a giant unified block. Many of them fought with each other bitterly for contributions from the laity (there is more than a little competition involved in offering indulgences for pilgrimages and donations). In some cases, especially women's monasteries, it could be a fight for survival. The Reformation era is filled with propaganda about nuns in furs and nuns keeping male concubines, but the average picture of late medieval women's houses is not nearly so sensational. A wealthy and important convent in a city like Nuremberg would be characterized by its massive library, not the wardrobes of its nuns. With increasingly strict rules of cloister for women (that is, that women had to stay within convent walls and not work outside/go outside to sell the work they made inside), many if not most women's houses were actually financially struggling. And numerically speaking, "the clergy" in the Middle Ages predominantly meant local parish priests--many of whom received so little money for their religious work that they held an ordinary artisan or agriculture job on the side.

The most important thing to remember about the possibility of deceptive clergy, I think, is to consider those pivotal 1520s. Some clerics fled the now-Catholic Church for baby Protestantism; some remained. Some lay people fled the now-Catholic Church for baby Protestantism; some remained. Of course, that choice wasn't always a choice, in the end, but you can find people who resisted on both sides.

I'm a medievalist because the Middle Ages are the best ages, but the early Reformation is possibly my favorite specific moment in history. As Diarmaid MacCulloch so lovingly details in The Reformation: Europe's House Divided, it's a time when you can see people's ideas and beliefs--on all sides--actually changing history.