Wow, that is a lot of big questions right there so lets break this down a bit. You are essentially asking three separate questions: A; how common are wars really, B;How do wars typically effect populations, and C; Why does it even matter whats happening abroad?

It is often quoted the War is simply politics by others means but I would assert that war is economics by others means. Now there are many different schools of historical interpretation but I tend to lean toward interpretations which focus on larger trends and understanding complex systems and through this lens the causes and context of wars can be understood. Obviously when two peoples go to war it is out of some sort of competition; no one goes far away from home to kill other people and risk death lightly, you need a pretty good reason, and this reason is usually competition over resources. From ancient Rome to World War II men have been fighting each other for land and water. When Rome fought Carthage it was largely a fight over economic control over the mediterranean (this is not a post about the causes of the Punic wars so I'm not gonna get bogged down in specifics with this). It could be argued that the World Wars were fought over ever increasing scarcity of resources due to huge explosions in productivity and population. Hitler's Lebensraum was his desire to acquire land for Germans to work in order to sustain or increase economic output. Even wars that don't look like economic wars may well be. The Trojan War according to legend was gought over Helen of Troy but perhaps Troy's location at the gates to the Bosporous gave it economic advantage over the greek cities through its access to the Black Sea and helen of Troy was simply a Casus Belli.

In this view it is quite understandable that Wars happen frequently. Mankind is constantly consuming and producing resources within a chaotic and dynamic system known as the economy. This creates pressures between tribes which often come to blows. It has been argued that war fare is mankind's natural state and historically that does seem to be case whether its low intensity conflicts like those the Philippine Insurrection or large scale conflicts like the 7 Years war conflict does seem to be ever present.

So to anser your first question; yes, history is just chock full of wars. People are constantly in conflict and only in the most recent history has this seemed to subside somewhat. But how do wars affect populations? This is somewhat more difficult to answer because the range of human experience is so vast and obviously some conflicts have very little effect on the average person and some have enormous effects. Once again I would argue that all conflicts have an effect on the populations involved simply due to the fact that all conflicts are economic in nature to one degree or another. It is quite apparent that enormous conflicts like WWII devastate their populations, 500 years of germanic settlement on the Baltic coast ended in 1945 as the Russsians pushed westward toward Berlin, according to John Keegan 7,000,000 Russian Civilians died (Keegan, The Second World War). But smaller conflicts can also influence everyday civilian lives. The War of the Roses was largely fought between landed nobles but that does not mean that the everyday population was not affected. Though it is hard to quantify from the sources available a state surely cannot continue to function properly when its Monarch is dethroned and another is instated as happened when Richard III assumed the throne. Far off conflicts can have enormous economic impact on populations thousands of miles away as well. As the spanish conquered the Americas and began mining vast amounts of silver to be transported back to their capitol little did they know they were wreaking havoc on the Chinese economy. As the galleon trade expanded spanish silver inflated the chinese economy so much that their system of currency essentially collapsed leading to economic catastrophe (Charles C Mann, 1943).

Certainly in places like ancient Rome foreign wars would have felt very close to home especially during the republic when men were required to go fight as part of their civic duty. All but the poorest citizens had to furnish their own armor and weapons and were required to follow the Consuls to war when called upon. During the early republic campaigns may have only lasted a few months as the Romans went to fight the Sabines or Etrsucans but as distance to hostile land grew so too did lengths of campaigns and eventually men would be gone for whole growing seasons or even years. This led large land holders to essentially annex land owned by men on campaign. In more modern times we have small, standing professional armies but similar impacts can be felt as well as others. Eisenhower famously stated that every dollar that goes toward building a battleship is one less dollar available to build a school. The economic impacts of all conflicts and potential conflicts affect everyone either directly or indirectly.

I think I have answered your second to questions in one response just now, I didn't mean to but it worked out that way because the reason these conflicts matter is because they do affect everyone. Whether you are a peasant growing rye whose farm gets devastated by foraging armies or simply an american tax payer during the cold war funding massive military infrastructure war has a long reach on all societies.

Just so you know, your question is as much philosophical as it is historical, because the question of "what would a peaceful time have been like" involves delineating exactly what one means by peace. And then we can end up in debates over things like the nominalism vs. platonic ideals, or foucauldian ones over "who gets to decide what is a peace/war," or simply linguistic ones over how different cultures and languages frame whatever is closest to "peace" as a concept.

For example, if you only think of peace and war as binary states in opposition, then whatever is one is "not" the other, but you still have to define at least one of them. And the problem of war (and peace) is there are always "features" of war and peace that overlap can overlap in any time frame.

The fact that so much historiography is dedicated to war, is a reflection of the function of pre-modern historiography, which focuses on the elites (who were able to have access to literacy), and war as a conflict of elites against each other, utilizing their resources (people under their control). War and peace were defined quite easily then in contrast to our connotations now. Either you are in a state of conflict with another group of elites or you aren't. But now, you have to deal with groups of people who aren't in open states of conflicts, or groups of people not easily delineated, or violence that isn't clearly delineated. What then?

As we spread beyond that concept of historiography, then war and peace cease having such clear defining boundaries. Then you have to deal with violence in its totality, the aims of such violence, or sometimes (as in cold wars) the lack of clearly defined violence in general.

Which is probably where your confusion comes from. You, as a popular reader, are sitting on the nexus of classical historiography (which focuses on elites, and their conflicts) and modern historiography (with its wide breadth in scope on social, economic and cultural affairs).

These are good questions to ask, and in fact, that question "what would the common people have been able to perceive", is precisely what historians now are attempting to expand upon.

Just treat your question as a sign that those efforts are succeeding, and continue asking them of yourself, and the histories you read.