The country and people surrounding a fortified centre were just as much a target as the fortification itself. The answer to all your questions is "yes".

I'm sorry to say I can't talk in depth about the Hundred Years' War, so you'll have to make do with an answer about Classical Greece. In the context of that period (as in many others), the main thing to bear in mind is that sieges are extremely difficult and expensive operations. In order to assault a fortified position or town, troops and engines have to be deployed against the enemy's best efforts to fend them off, and many men are likely to die. In order to starve out the defenders, a full encirclement of a fortified centre has to be maintained for months or even years. Neither of these things were easy to achieve, especially in an era or relatively small armies drafted from ordinary people who had no military training and who had their own farms and workshops to get back to. For the attackers, unless their army consisted of leisure-class men or mercenaries, a long siege was impossible and a siege assault wasteful and all too often pointless. For the defenders, hiding behind strong walls with a big food supply seems like a pretty safe option; it will be all but impossible for the enemy to hurt you.

So how do you hurt an enemy whose fortress you can't break, and who refuses to come out and fight? Simple: you attack the things they can't protect. Farms, fields, and agricultural infrastructure (irrigation canals, mills, oil presses) are excellent targets for destruction. Flocks can be led away; crops can be trampled; trees can be cut down; farmhouses burned, wells spoiled, etc. etc. Anything that can be carried can be stolen. In addition, it was normal Greek practice for war captives to be killed or sold into slavery.

This form of warfare had several advantages. First, it could be presented as a sufficient goal in itself; since major urban centres were rarely captured in Classical Greece, the mere opportunity to ravage a significant part of the enemy's land was considered a worthy achievement for a campaign season. The enemy had been hurt and humiliated, and their property had been reduced, to the enrichment of the invader. We are told that Thebes benefited particularly from the Spartan devastation of the Athenian countryside in the Peloponnesian War, since the Spartans went to Thebes to sell all the loot:

They bought up the slaves and the rest of the stuff captured in the war for a low price, and, since they lived nearby, they carried home all the equipment from Attika, starting with the woodwork and the rooftiles of the houses.

-- Hellenika Oxyrhynchia 17.4

Second, it could destroy an enemy's harvest for the year, which could have devastating consequences in a subsistence economy. There are several examples of Greek states brought to their knees by just 2 consecutive years of crop devastation. An army had to be quite large and stay in the field quite long to achieve a sufficient level of damage, but the chance to win the war without any real fighting was always worth the effort. Even a state as large and powerful as Athens was not expected to be able to survive the systematic devastation of its countryside:

At the beginning of the war, some thought the Athenians might hold out one year, some two, but none more than three, if the Peloponnesians invaded their country.

-- Thucydides 7.28.3

Admittedly, ever since the publication of V.D. Hanson's Warfare and Agriculture in Classical Greece (1983), the question of crop devastation has been controversial. Hanson argued that it was not possible for Greek armies to do significant damage to vines or to cut down olive trees with the tools they had to hand, or to effectively set fire to grain crops (except for a very small window of time just before the harvest). As a result, ravaging and devastation must have been more symbolic than actual. The source I've just cited seems to disagree, and there are several others, but it should probably be understood that the ravaging of the countryside was often much less severe, less all-encompassing and less permanent than our sources would lead us to believe.

According to Hanson, the real reason for the ravaging done by Greek armies was its third major advantage: it might provoke the enemy to battle. This would allow the attacker to avoid the ordeals of assault or siege, and deny the defender the advantage of a strong fortified position. It might seem foolish for a defender to leave his walls and towers to go fight the enemy in the open, but the frustration and anxiety of a farming population forced to watch as its land is destroyed cannot be underestimated. In his account of the Peloponnesian War, Thucydides gives us a taste of the mood at Athens:

When they saw the Spartan army at Acharnai, barely seven miles from Athens, they lost all patience. The territory of Athens was being ravaged before the very eyes of the Athenians, a sight which the young men had never seen before and the old only in the Persian Wars; and it was naturally thought a grievous insult, and the determination was universal, especially among the young men, to sally forth and stop it. Knots were formed in the streets and engaged in hot discussion; for if the proposed sally was warmly recommended, it was also in some cases opposed. Oracles of the most various import were recited by the collectors, and found eager listeners in one or other of the disputants. Foremost in pressing for the sally were the Acharnians, as constituting no small part of the army of the state, and as it was their land that was being ravaged.

-- Thucydides 2.21.2-3

This passage also answers your first question. The population of farms and villages outside of the main urban centre would generally seek refuge within the walls. Greek cities tended to have very large walled circuits, often encompassing not just the built-up centre, but also various sacred and public spaces, as well as some farmland; in the event of a siege, much of the open area within the walls would be covered in temporary housing as farmers and their families and slaves sought to weather the storm. The source I cited above on Thebes during the Peloponnesian War is very explicit about this:

When the Athenians began to move against Boiotia, those who lived in Eurythrai, Skaphai, Skolos, Aulis, Schoinos, Potniai and many other such unwalled places were gathered into Thebes, doubling its size.

-- Hellenika Oxyrhynchia 17.3

If there was a proper siege, this would obviously put enormous pressure on available food supplies. The Athenian example shows that it also caused tension within the city, because the interests and preferred policy of those from the countryside didn't always align with those from the city. However, fundamentally, this is why walled centres existed in the first place. Sometimes those who lived too far from the main city would gather into local forts and fortified places, which was also often where flocks of sheep and goats would be kept from the invaders.