The objectives of a war would vary depending on what the political goals were. Putting down a rebellion or seizing a small amount of territory would have more limited objectives than a major war. The goals of battles in the Wars of the Roses were often as much about defeating major enemy leaders and killing or driving them from the field. Cities might be taken, depending on the purpose of the war, but sometimes defeating a particularly important enemy leader would end the war right there. The capture of Francis I at Pavia in 1525 eventually led to him signing the Treaty of Madrid and the withdrawal of most French troops from Italy.

Despite the emergence of cannons as an important part of siege warfare in the late 14th and early 15th centuries, cities and fortresses were still strategic assets and continued to be constructed. Contrary to what some scholars have asserted, the invention of cannons did not instantly reduce all fortresses to dust. Defenders also adopted the cannon, modifying towers to mount cannons of their own. There are plenty of sieges which failed despite the presence of cannon, which shows that gunpowder alone was not a guaranteed war-winner. Cannons certainly made sieges easier to conduct and perhaps more viable, but the number of sieges of fortified cities that took place during the Thirty Years War in the 17th century shows that fortifying a city was still a useful and necessary expense.

Do you mean "knights" as in the social category of knighted men or "knights" as in the military sense of heavily armored troops? Although some scholars have seen an increasing tendency for men of knightly rank to participate in warfare less often through the 15th century, plenty of formal knights still fought or commanded men in battle. As for the broader category of heavily armored mounted troops, yes, men-at-arms (who could, of course, dismount to fight as heavy infantry) continued to be a vital and necessary presence on the late medieval battlefield. The units of lances which formed the basis of the reformed Burgundian and French standing armies in the late 15th century still saw the man-at-arms (in plate harness) as an important component of the military. I wrote a little about the reforms of the late medieval French military system here.

English archery laws remained in place well into the 16th century. Although by the 1540s, the time of the longbow had clearly passed, in the late 15th century, archery still played a major role on the battlefield. The presence of large numbers of longbowmen was a constant feature of the battles of the War of the Roses and most literary chronicles of the various battles attest to hails of missiles from both sides preceding any engagement.

Armies became increasingly professionalized over the course of the late medieval period. Contracts of indenture were the primary mechanism for all ranks of English armies. The French also used contract troops to assemble armies that contained both aristocratic retinues and free companies of professional soldiers. The process of creating standing forces in France during the mid 15th century was not so much an act of creating new soldiers from scratch, but of amalgamating pre-existing groups/companies into a more coherent organizational scheme and consolidating them under royal control. The English never really made the leap into creating a full-on standing army of their contracted professional soldiers. Instead, the war of the roses was fought primarily by enormous groups of retainers and men who had been granted livery (usually including pay and food) by prominent aristocrats in exchange for military service. These private armies were the main source of soldiers for the English monarchy, but also represented a threat to the stability of the kingdom. Under the Tudors, the practice of granting livery was increasingly restricted, but no centralized military system was established in its place. Despite much nationalist posturing about the defeat of the Spanish Armada, English military history in the 16th century is a rather pathetic and inglorious record when compared to some of the major victories and campaigns of the 14th and 15th centuries.

I'm not very well-read on law enforcement in the period, so I will refrain from trying to speculate based on the bits and pieces I do know. Perhaps /u/sunagainstgold has some insight on that subject to share?