1. Not necessarily. I would say that humanism became prominent in Florence because of its comparatively high literacy rates due to the commercial revolution of the 13th century. In his history of Florence (Full citation found in book list on this subreddit), Najemy suggests that at least 60 percent of the population had at least a working level of literacy during the high and late Middle Ages. Furthermore, we can easily demonstrate that Humanism has its roots in commerce and the literacy that it necessitated.

Petrarch is considered the first humanist. He came from a long line of notaries and his father was a notary. This position within Italian society was extremely important as these men could draw up legal contracts such as commenda type contracts that helped to foster international trade. Furthermore, notaries would have been absolutely crucial to building up the fortunes of the great banking compagnia that were needed to develop patronage networks. The connection to literary genres and notarial activities is even more explicit if we consider the fact that Giacamo da Lentini, a notary in the service Frederick II (1194-1250), invented the poetic form that Petrarch perfected.

This is not to say that republicanism was not important to the creation of humanism. For example, Cicero, Petrarch's hero, was an ardent republican (at least in the eyes of the Renaissance humanists). That said, many of the great works of the Renaissance were created during the period of Medici dominance, when Republican government in Florence was a sham. Indeed, the humanist poet and playwright Poliziano was a Medici lackey/adviser. Furthermore, within Florence, Venice was considered to be the paragon of republicanism. When Savanorola tried to reform the government to become more republican, he looked to Venice for a model.

It should also be noted that after the initial flowering of humanism in Florence, the movement flourished in cities that were ruled by authoritarian governments. In reaction to the crises of the 14th century, many Italian cities abandoned the commune form of Republicanism and appointed strong men to guide their people. These men are referred to as signoria, but they sometimes go by different names such as capitano del popolo in Genoa. This form persisted in many small cities (and Milan) where humanism was embraced. Humanism wasn't universally accepted in the smaller cities of northern Italy, For example, there is some debate as to whether the artistic production of Pisanello is truly main line "Renaissance" art or an evolution of the International Gothic that developed somewhat earlier than Renaissance art. Regardless, we can say that Sigismondo Malatesta, the despot of Rimini, created a circle of humanists in his court circle that was completely cut off from civic society. Check out images of the Temio Malatestiano for visual evidence of this.

2. Kind of, but I think you're missing one of the crucial aspects of patronage. Patronage was most often a personal matter, rather than a matter of state. For example, one of my favorite works of Renaissance art is Masaccio's Tribute Money in the Brancacci Chapel. http://www.christusrex.org/www2/art/images/masacc04a.jpg. This painting was commissioned in the 1420's, when the Florentine government was attempting to institute the catasto or income tax. I argued in a seminar paper (and my professor, a former curator at the Uffizi, agreed with me) that this painting is a reaction to that tax.

There is a myriad of examples of patronage being used to further individual political interests. I will add one more here. When Cosimo di Medici was planning his return from exile, he began commissioning art in monasteries outside the city walls and gradually circled inwards to the city center until he was commissioning works of art within the city itself.

This doesn't mean that art didn't have a martial value, but not in the way you are thinking. The statue of St. George in the niche at the Church of Orsanmichele was created during one of a series of lengthy wars between Florence and the Visconti of Milan: http://arthistorygalore.files.wordpress.com/2011/04/donatellos-st-george.jpg. The statue was meant to exude confidence and bolster the war effort. That said, it was commissioned by the metalworkers/armorers guild, not the government.

This brings me to my last point about patronage. Besides having political motivations, patronage could be used to sell things. The Arte di Calimala, or cloth finishers guild commissioned tons of great art, including Ghiberti's beautiful doors on the Baptistry of San Giovanni di Baptismo. They also commissioned this statue of John the Baptist in another niche of Orsanmichele, http://www.bluffton.edu/~sullivanm/orsanmichele/0007.jpg. The figure is seeming to hold out his beautiful robes to show the people of Florence. The reason for this position is not limited to commercial concerns, the influence of International Gothic and the billowing, complex clothing that was an important trope of the movement, certainly prescribed the depiction of the Baptist's clothing. That said, the two motives are not necessarily mutually exclusive.

3. I'm not so much interested in the Renaissance north of the Alps, but I'd agree with you. That said, I'm a historian of Italy and naturally biased. Thinkers in Northern Europe had some new ideas, but I wouldn't necessarily say they took it further. I'll let someone else without a chip on their shoulder take this question.

4. Your fourth question kind of alludes to one of my biggest historical pet peeves (I'm glad you asked the question though!). The consequences you list are related to the period in which the Renaissance emerged that were not necessarily direct consequences of the intellectual movements. I think that it's very important to remember that the Renaissance was an intellectual movement that emerged in Italy during the Middle Ages and spread north of the Alps in the early modern period. The reason for this is that we don't talk about a Neapolitan Renaissance, a major city in the same peninsula as Florence. Indeed, Antonello da Messina left Sicily and southern Italy because he couldn't find sufficient patronage there. Furthermore, we talk about the English Renaissance, but that occurred well after the original genesis of the movement in northern Italy. Thus, I would say that although the Renaissance and humanism had an effect on the voyages of discovery, (Christopher Columbus was Genoese and fifteenth century Genoese humanism is a very underdeveloped field of study), they aren't direct consequences of the movement.

I do think that the development of a philosophy of humanism and republicanism is the most important aspect of the movement. By the time the barbarians in England (sorry English historians, had to take a pot shot :)) finally caught on to the movement they incorporated the philosophy into their theories of government and constitutional monarchy.

Sources, Najemy's history of Florence, a graduate seminar in Renaissance art, in which we used Campbell and Cole's Italian Renaissance Art as the textbook, and years of research into 14th and 15th century Italian social history. If you need more citations, I can probably dredge some up from my Zotero account.