The Nazi's didn't surrender because Hitler insisted that the country fought on. Even as Soviet soldiers flooded Berlin, Hitler (supposedly) was still so delusional that he believed that Germany could still rise from the ashes and win the war in some shape or form. In all honesty, by this time, Hitler was mostly insane. When his fellow officers pleaded with him to at least let the women and children be evacuated from Berlin, he said something along the lines of that even they should fight or die. He meant to drag what remained of Germany down with him, largely because I think he believed that a non-Nazi Germany is not worth surviving the war. This is a major reason for why Goebbels and his wife committed suicide along with their children; because they feared defeat, and because they did not want to live in a non-Nazi Germany.

Nonetheless, while Hitler went along being delusional, there were elements in Germany at least trying to soften their defeat, make it less disastrous in the end. While Hitler was still de facto leader, many in Germany were insubordinating him by this point. In particular, Heinrich Himmler, on April 22nd, offered Germany's surrender to the Western Allies (but not the Soviet Union.) In the last months of the war, much of what remained of the German military dedicated itself to protecting refugee columns and guiding civilians. The Soviet mass rolling over Prussia and Eastern Germany caused massive amounts of hysteria and panic, and civilians were fleeing en-masse from the Soviets. The German military ended up dedicating a lot of its remaining manpower to holding off the Soviets simply so German civilians could flee West and be taken captive by the Western Allies over the Soviets.

A particular German General, Walther Wenck, who become known as "The Boy General" due to his young age, commanded the German 12th Army in the Battle of Berlin. He committed most of his efforts to aid thousands of German refugees in escaping the rear elements of the Red Army. Basically, he took what remained of his army, what remained of the German 9th Army, to the Forest of Halbe. He used his forces to force open an escape path through with thousands of German civilians then flooded through across the Elbe and into territory occupied by the U.S. Army. This has been estimated to have allowed almost 250,000 civlians and 25,000 soldiers of the 9th Army to escape the Soviets and reach the Americans.

Sources:

Berlin: The Downfall 1945 by Antony Beevor

EDIT: And, right, your bonus question. The idea that a country would "fight to the bitter end" is actually a somewhat modern conception based off of modern examples of Germany in WW2, Britain in the Battle of Britain, and the Soviet Union not giving up in the wake of Operation Barbarossa. Realistically, countries have become accustomed to fighting longer, more devastating wars that could bring them to the edge largely because of how advanced warfare has become. The concept of "Total War" originated as early as Napoleon, and took a firm hold over how warfare was conducted in the American Civil War and the First World War. The whole idea is that when you throw your entire country behind the war, man, money, resources, all of it (as is the nature of a Total War), giving up would be counterproductive to all of the men, women, and resources you have so far lost.

To give you some examples, in the American Civil War, over 600,000 men (both sides) died by the end of the war. So much manpower and resources were thrown into the war by both the North and the South, that neither of them surrendering looked likely until there was no other choice. The South likely knew that victory was slim even from the very beginning, but it took the fall of the Souths western armies, the occupation of much of the south, and the fall of Richmond to finally convince them to surrender.

In WW1, all of the combatants suffered greatly in the war. It was one of the first "true" fully modern and fully industrialized wars where entire populations and economies were mobilized to back the war effort. Many countries were so depleted and exhausted by the end of the war that it caused the recession of the strength and power of Europe in the Interwar Years. France in particular suffered immensely in the war, they lost nearly as many men as the Germans, and had the entire Western Front take place on and devastate their land. But by 1917, even as the Germans started their "Spring Offensive" and begin to push the Western Allies back a bit, the French could not surrender after all of the men and women they lost in the war, all of the resources that were lost, many cities and towns laid waste. There was a lot of defeatism among the French, but most agreed that at this point, surrendering would render all of their sacrifice meaningless, for the lack of a better explanation.

Austria-Hungary definitely could have surrendered much earlier in WW1. Unfortunately for them, they were very weak in the war and became a German satellite by the end of the war. They didn't have any reserves, and suffered the brunt of the Russian wrath in the war. They bled and died on the Italian Front, and "the spine of the Austrian Army" was for all means and purposes, broken, in the Russian Brusilov Offensive of 1916 (considered as one of the most lethal offensives in history, and much of it was aimed at Austria). By all standards, such a beating wrought upon Austria in this attack could and might have have wielded capitulation from other countries, but by 1916, too much was committed to the war to give up so suddenly.

Basically, the more men and resources a country dedicates to the war, the less likely that they will surrender or give up down the road. In a Total War, where huge chunks of your population disappears as casualties and reserves of your resources vanish and whole towns and cities lay in ruins, just giving up would render a the meaning of these sacrifices less meaningful. A country like France could not see itself give up in WW1 unless there was no alternative because all of the men that died beforehand would have, in a way, died for nothing. Germany in WW1 could have afforded to surrender largely because not much of the war took place on their soil, save for the fighting in Prussia and East Germany on the Eastern Front. Their industry, cities, and towns were all largely intact, their home soil largely undisturbed. Their sacrifice was mainly men and resources, and they accepted their likely defeat in the face of their odds.

I am not as researched in earlier wars (anything before the mid 1700's) to tell you why they went on for so long (ex. The Thirty Years War, the War of Spanish Succession (~13 years), The Hundred Years War, etc), other than that it might be attributed to the fact that forces in these times were nowhere near as mobile, and were generally very slow. Wars back then were also waged by the country and not necessarily as a whole. In a war, peasants and farmers would keep farming like usual and would occasionally be raised to fight, but the entire weight of a country in the terms of the modern definition of Total War as we know it today, was not exercised back then as much.

I hoped I was of some help.