Germany had so many successes prior to their invasion of the Soviet Union but I've read that so many mistakes were made after they tried to invade.
Germans could actually see Moscow (from what I've read)...why not take the city? Wouldn't it have been demoralizing to the enemy to take the capital?
While Moscow was an important industrial, population and administraitve centre, and an important railroad hub (as can be seen in this image), it was not critical to the Soviet war effort to the extent that they would be unable to continue to fight without it.
There were other population centrals, other railroad (and river and canal) transportation lines and much of the industry were being built up on the other side of the Ural mountains after being evacuated as the Germans advanced.
Heeresgruppe Mitte had advanced very far, outrun its supply and its own infantry in late July, early August 1941. It was dangerously exposed to a counterattack, especially from the south, as Heeresgruppe Süd had faced mors stiff resistance and was the weakest of the three Heeresgruppen.
The Germans believed that if they knocked out the initial strength of the Red Army, the Soviet state would collapse on itself, a bit like Imperial Russia had in 1917, thus they directed the mobile forces of Heeresgruppe Mitte south to help Heeresgruppe Süd complete the encirclement of a majority of the Soviet forces in the Ukraine around Kiev while the infantry divisions of Heeresgruppe Mitte caught up with the front and secured the flanks.
Once the mobile forces were back, supply problems and autumn rains turning the ground to mud stalled the German advance further, and when supply had been brought up and the ground frozen enough for the German armoured forces to move again, the Soviets had brought up extensive forces, both newly raised and from their strategic reserves in western Siberia (Kazan to be specific).
The huge distances, the ruined infrastructure, the less than stellar German logistics planning and the fact that Soviet railroads run a different gauge compared to European ones all added to the German supply problems, to the extent that they had to choose between delivering ammunition, fuel and food and winter clothing to the frontline troops.
It is hard to see how the Germans could have acted differently - what they did accomplish was extraordinary and a testament to the tactical flexibility of the German army and the lack of the same in the Red Army at the time. However, they failed to prepare for a long war, failed to plan properly for logistics and supply and were overly ambitions about the war's progress as well as severely underestimating both the staying power, the ability to absorb casualties and the ability to keep raising, equipping and supplying troops of the Soviet state.
Antony Beevor said that Hitler wanted to avoid the assault of a big city, for the human losses that meant. However in 1942 he attempted the assault on Stalingrad with catastrophic results already known.
So it is July 1941, when Hitler could continue forward with the AGC (army group center) from Smolensk to Moscow. The AGC had to pause in his attack because of their logistical problems (the AGC supply needed 45000 tonnes, only 30000 could move the hard Soviet roads, -RS Stolfi "Hitler's Panzers East")
In August 1941 the Yelnya Offensive was a reminder to the OKW that without securing the flanks was absurd to attack Moscow. The AGS (Army Group Sotuh) did not have it that easy for the attack in Ukraine. So a counter attack in Moscow from the south was a real threat. On the other hand Kiev City would not be defended with the same intensity that Moscow would be, and Kiev did not suffer the vulnerability to receive counterattacks down the flanks and also meant a hard blow for the Red Army.
Moscow was not an easy target. It was not going to be encircled with the ease that were Minsk and Smolensk.
Minsk, Smolensk and Kiev, all major cities fell similarly; surrounded by panzer division, and the troops once looked out of supplies and ammunition surrendered. There was no assault as at Stalingrad where Paulus could not encircle the city.
The likelihood of achieving the encirclement of Moscow was low because:
Without encirclement a total surrender of Moscow was not likely to happen. It was a logical decision to attack Kiev instead of Moscow.
your second question could be better for /r/HistoryWhatIf/ . About that I will only say that the OKH before Barbarossa concluded It was not enough to take Rostov + Leningrad + Moscow to make surrender the USSR. The real mistake of Hitler was to attack the USSR, the second was to no make a peace agreement after the fall of Kiev, he could easily get Ukraine + the Baltic On hindsight I would asked for those terms. Hitler never though on them because he wanted the unconditional surrender of USSR. Still was a possibility in the minds of Mussolini (WEGNER B “II. Bundnispolitik und Friedensfrage” en MGFA “Das Deutsche Reich und der Zweite Weltkrieg. Bd.8. Die Ostfront 1943/44”. Deutsche Verlags-Anstalt (2007) p.51-3) and Stalin(Stalingrad of Anthony Beevor)
Since other folks have already explained the strategic problems of taking Moscow, I thought I'd contribute by pointing out how it would look like for your average German infantryman (Landser).
One of the major misconceptions about "infantry" Divisions is that they consist primarily of infantry. People think of them as formations of 10,000 men, each with their own rifle.
This was in fact not the case with the German Army. In fact only around 3,500 of a Division's total complement of 16-17K was frontline riflemen. If we add machinegunners and other heavy weapons troops who might see frontline combat, then the total is around 6K+. Hence, this means only around a third of an infantry Division actually saw regular frontline infantry combat.
The majority in fact manned the supply services and the heavy weapons/artillery. Those machine guns need people hauling ammunition for them, while artillery fire can destroy large enemy concentrations or defenses. This is in fact a big reason why the German Army inflicted so many losses on the Soviets while taking so little in return - the Germans in fact used their big guns and heavy weapons to decimate the Soviet infantry; who were largely ill-equipped with heavy weapons and couldn't respond in kind.
The problem for the Landser in December 1941 is that despite relatively light total Wermacht losses - each Infantry Division was only around 10% understrength at this point - most of it was borne by the frontline infantry. Indeed in most cases as much as half of the rifleman complement of each Division was already gone. Shattered units had to be disbanded and used to reinforce stronger ones; or worse supply troops with inadequate skills were being used as replacements.
For an Infantry Division still fighting field battles, this was still an acceptable situation. They simply redistributed the machineguns to fewer men who would hold and pin the Soviets while the artillery continued to be the main killer. However, this was a completely untentable situation for an Infantry Division attempting to attack a city. Your average Landser, who had already lost half of his squadmates on the road to Moscow, were now going to be asked to attack an entrenched enemy in an urban environment. This is terrain that greatly favored the defender and where more frontline casualties were inevitable - casualties that the infantry could no longer sustain.
Moreover the heavy weapons which supported the Landser previously were now greatly reduced in effectiveness - artillery having trouble demolishing buildings and in any case the opposing infantry are often positioned so close together that the risk of friendly fire was too great. Most assaults will be limited to using only firearms and grenades - allowing the Soviet soldiers to fight on a largely equal footing.
This disparity, in fact, was probably behind the oft-cited "superiority" of the Soviets in city fighting. It wasn't necessarily because the Russians had a racial bonus to city fighting like video game logic dictates. Rather, it was because their Divisions had much more infantry than heavy weapons; and heavy weapons were largely nullified in a city fight. This disparity was confirmed in Stalingrad, wherein Soviet infantry-heavy formations suffered huge losses but were able to frustrate the German assaults that were reliant on heavy weapons.
Moscow in 1941 would have been little different. Indeed, with most of the frontline outfits already at half strength it would have been widely seen by the Landser as suicide - there just wasn't enough skilled infantry left to make such an all-out assault.
Another question: Did Soviet leadership have any plans if Moscow had been taken or the Soviet military was defeated?