I discovered craft beers some years ago, but I've been always been amazed by Belgian brewing culture, which is so different from German and Great Britain traditions.
Why is it that beer has such important and diverse roots in Belgium? What are the historical reasons?
When one speaks of "Belgian brewing", one must distinguish between two major styles of beer: the famous abbey ales produced by Trappist orders in Belgium (and now one in America), and the the saisons and bières de garde produced as inexpensive nutritional supplements and dietary staples for farm life. An interest in the history and production of these beers is best served by Phil Markowski's Farmhouse Ales and Stan Hieronymus' Brew Like a Monk.
To touch on a few of your questions:
As previously alluded, beer served a utilitarian purpose as a dietary staple and nutritional supplement for an agrarian society. Beer was frequently brewed in large batches at regular intervals in support of farm life, and the result were table beers and saisons for work during the harvest and bières de garde (loosely translated: "beers for keeping") to survive the winters.
Abbey ales are not as varied as they initially appear. Much of the variation in beers brewed in Trappist style come from fermenting different "runnings" of the same batches of wort (unfermented beer); to summarize very briefly, the strength is dependent upon the sugar content which is dependent on how many times the mashed malt has been "rinsed". See Wikipedia's page on lautering for more details.
Belgian and English brewing are actually not very dissimilar from a historical perspective, and there was quite a bit of overlap in technique between English, Belgian, and Flandrian brewers. The differences in style we perceive now (e.g. IPAs vs Flemish sours) evolved by regional taste preferences from common roots: malt-forward beers (which were originally quite sour) using the low alpha acid noble hops which thrived on the continent. Consider the similarities in taste and composition between an ESB and a dubbel.
In addition to the above referenced works, a quick read through the history section of Jeff Sparrow's Wild Brews should answer any remaining questions you might have about the history of Franco-Belgian beer.
Brewing in monasteries did a lot to keep brewing more of a passion thing than big business. The monks of the Trappist monasteries were largely concerned with just keeping afloat and contributing to charitable works than expanding and making huge piles of cash so their brews don't need to worry about using using malts that are too expensive or things like that. It stopped adjunct malts from showing up in the brews and watering them down.
By the time worldwide distribution became a thing their own styles had been engrained for so long that high quality beer had become a tradition that nobody was willing to leave behind. Sure there are some crappy beers like Stella Artois, but the vast majority of Belgian beer is awesome stuff like Chimay, Corsendonk or Rochefort now.
There's also a pretty big culture there of pairing beer with food and even cooking with beer. Its just deeply engrained in every day life for them, not just as a way to get drunk and be merry but of simply enjoying your breakfast.
A couple other things contribute to the Belgian beer culture:
Entschuldigung an Deutschland.
Trappist Monks sold beer to support the monasteries. There is no order for the monks to abstain from alcoholso they use the money raised to support the monks and the abbey in which they live. People really liked the unique flavors of the Belgium Trappist Monk's beer and it became its own style.
Most of the time you will see home-brewers air-lock their fermentors so wild yeast cannot spoil the beer. The strains of yeast that have been cultivated for centuries inside the abbey walls have given the Belgian beers their unique flavors.
