Although a piece of popular history, the lecture series "The Story of Medieval England" by Professor Jennifer Paxton that I've just read and listend to, has a chapter which deals with your exact questions, which I partly will be citing and paraphrasing.

Is the importance of courtship just a result of romanticizing the Medieval Period or did suitors really try to woo one another with love poetry and such?

Rather, it's a result of "romanticizing" during the Medieval Period itself, and answering your second question seems a bit tricky.

In the 12th century, the idea of courtly love became popular in song and literature, precisely because it provided romance, while marriages at the time were indeed alike to business arrangements (which doesn't mean that there were not plenty of cases, were noble spouses were indeed enamored with each other).

It may be helpful to think of entertainment today. You have pieces like "50 Shades of Grey" for the female, and... pick whatever spectacle of violence for the male, audiences. Elements from both would be as objectionable in reality, as they can be appealing as a fantasy.

Similarly - even regarding today, how would you go about generalizing the way that people woo each other?

Courtly love is potentially adulterous and exists across social boundaries - absolute taboos which in reality would have grave consequnces, yet the fantasy of it was appealing for various reasons, despite or because of the taboo.

The tension between fantasy and reality was certainly sensed by contemporaries.

"One of the most famous works of this period was written at the court of Marie de Champagne: Andreas the Chaplain’s The Art of Courtly Love." [...] Andreas lays out how men and women of different social classes should approach each other to try to win each other’s love. [...] Then, after spending an entire book describing secret, adulterous relationships and how to conduct them well, at the end of the book, he takes it all back. We don’t know whether it was meant seriously or in jest, but it brings us to a larger question about courtly love in general: Did people really engage in these kinds of relationships? Or was the whole point of the genre the vicarious thrill?

It seems like your question has no certain answer.

It's worth noting that the female characters in love poetry are in a position of power, she could reward the advances, or reject them, invoke despair, or inspire hope, in contrast to noblewomen being mostly bound by obedience to her father/husband/family.

It's also worth noting, that Eleanore of Acquitaine, the person to whom much of the spread of courtly literature can be atributted to, comes across as having a rather willful character and independent nature, which put her at odds with her pious first husband LouisVII (including rumours of a relationship between her and her uncle), who got along so badly that their marriage had to be annulled.

The south of France, where the court of Eleanore's father, Duke William of Acuitaine was, was influenced by Muslim cluture via its proximity to Muslim Spain. Duke William

"was himself a troubadour poet, but he was also a patron to other poets. The court of Aquitaine attracted some of the best poets in southern France, all writing in this new style. This is the atmosphere in which Eleanor of Aquitaine grew up. She grew up listening to love songs, and she brought them with her when she married King Louis of France, sparking a new literary fashion. She also passed her love of this poetry on to her children, especially Marie, countess of Champagne, and Richard, who would one day be king of England, both of whom were strong patrons of literature themselves. "

So all in all it would seem there was an ambivalent relationship between contemporary morals, practices, and expectation.