My understanding is that most medieval warfare consisted of raiding to forage for supplies, enrich the raiders, economically and logistically weaken the opposition, and damage the legitimacy of the opposing warrior-aristocrats as peacekeepers. Pitched battle was risky and often not decisive, while sieges took either lots of time and supplies or costed many troops when attempting to storm the castle or being struck by disease, thus most commanders pursued the low risk and relatively reasonable reward of raiding while avoiding battles and sieges as much as was feasible while still attaining their objectives.
However, I don't really have a good mental picture of what this raiding and ravaging entailed besides pillaging all moveable wealth that can carried be out of vulnerable villages and towns, burning what couldn't be carried if it was advantageous, and otherwise abusing unarmed people in the region. Local magnates would have wanted to have their knights to defeat these incursions, if only to protect their tax-base and honorable reputation, which should have resulted in numerous small scale clashes between raiding knights and defending knights but I have no idea what these fights would look like. Perhaps this was a good environment for showcasing individual prowess, bravery, valor, etc.?
I have also heard that Western European armies in the Middle Ages were composed predominantly out of small or large groups of (semi-)professional soldiers whom, within these conroi/retinues/companies/etc., had usually trained and/or fought together as these groups before becoming part of a given army. It would seem intuitive that these smaller but more permanent groups would have been able to foot the training necessary to reliably execute sophisticated tactics that wouldn't be possible when having to work as part of the ad hoc armies of the period, and would have done so if it was advantageous.
I have seen medieval tournaments described as having been regarded as a form of military training for knights, as well as showy and sometimes lucrative displays of prowess. Did events like the melee, jousts, etc. reflect what knights would do during raids when they encountered one another?
The last question is prompted by a vaguely remembered claim stating that the feigned retreat was a maneuver used by knights in skirmishes and raids, often to draw pursuing forces into ambushes, and thus was a traditional and well-honed practice merely scaled up for use in cases such as the Battle of Hastings. It sounds like it would be most practical to limit battle tactics and maneuvers to those that these cohesive and trained but small units of troops are familiar with given that they wouldn't have trained to operate together as larger units as later standing armies would.
Very interesting questions! There's a lot to unpack here. I'm presently sick as a dog, so I'll just try to tackle the gist of it.
Certainly pitched battles were rare. William the Conqueror only fought one or maybe two, depending on where you draw the line. His son William Rufus fought one, and his other son, Henry I, fought two. But I think you underestimate how common sieges were. If sieges were the steak of medieval operations, raids were the potatoes: cheaper, and a good accompaniment. They could be used independently of sieges, or as a crucial part of supporting a siege. Before the siege, they weakened the enemy's position by denuding the countryside of food and money, and while it was going on, their proceeds helped to feed the army.
The tournament of the late 11th century through the 13th century was very different than what most people imagine it to be. Our mental image of it is very strongly rooted in 14th-16th century practices, in which the focus was on the joust, an individual combat between two mounted men before an adoring crowd. The high medieval tournament was first and foremost a mock cavalry battle and much less a spectator sport. Two sides, often composed of knights from the same territory (say, Normans against Angevins or Flemish) but under individual lords, squared off in a predetermined area of countryside. The fight typically began with a mounted charge, usually with couched lances. After the two lines met and the survivors rode through each other, they broke up into individuals and small groups chasing each other through the countryside. The goal was to capture, rather than to kill, though the latter was unfortunately common, which explains why several kings of England banned tournaments from their realm. Generally speaking, a knight would be unhorsed and/or beaten senseless and made to submit. Once captured, a knight had to ransom himself, his arms, and his horse back from his captor - or, if he could not do so, and the victor was unwilling to extend him credit, they were forfeit.
Skirmishes between small parties of horsemen would look very similar to this. In contrast to pitched battles, they would be a bit more free-form, especially since archers and infantrymen would less commonly be present. One of our best sources for this is the History of William Marshal, a contemporary biography of perhaps the most famous knight in 12th-13th century Europe. There are two passages that I recall as being particularly instructive. I'm barely functional at the moment, so I hope it's alright if I summarize rather than quote.
In the first instance, William was serving in the household of his uncle, Earl Patrick of Salisbury, in 1168. The Earl was then in Aquitaine fighting for Eleanor of Aquitaine in yet another of the Angevin wars against rebellious vassals. While escorting her on the road one day, Patrick and his men were attacked by the rebel Guy of Lusignan (yes, the guy from Kingdom of Heaven), his brothers, and their knights. The Lusignans fell upon them by surprise, and the Earl and his men had to scramble to put on their armor and mount their warhorses before the clash. Patrick rushed the queen and a small bodyguard off to a nearby castle and attempted to meet the enemy with his remaining men. But the Earl was quickly killed (supposedly, by a lance to the back, a scandalous occurrence), and his men were overwhelmed and scattered. William Marshal apparently went berserk with rage and grief at his uncle's death and charged heedlessly into the Lusignans. His horse was killed, and the dismounted William retreated to a hedgerow. He set his back against it, and "like a wild boar amongst the dogs," he slashed and cursed and threatened and dared the rebels to come within his reach. One snuck up behind him and through the hedgerow struck his unarmored leg, after which the young knight was captured.
In the second instance, a much older William was commanding the rearguard of Henry II's household troops as they retreated north from the army of his rebel son, the future Richard I. In order to overtake the much smaller (and thus faster) force, Richard had left his armor behind and pressed on with all speed with the vanguard. With no warning, the Marshal turned his small rearguard about and launched a sudden counterattack on the strung-out vanguard. Richard was caught unawares. William made for him with all speed, seemingly intent on striking a killing blow. Richard cried out for mercy, and William cursed him and drove his spear into Richard's horse, before riding off to rejoin the main body.