Hitler did not have a realistic chance to accomplish his objectives during World War II, they were too ambitious. The central dilemma faced by Hitler as outlined in The Wages of Destruction (Adam Tooze) was that Hitler was unable to defeat the British empire and Americans without access to a secure, independent base of resources, and the only place that could be found was in the USSR (N.b. it was expected that the Americans would be supplying the British with resources and industrial goods, even if they didn't intervene outright). But the same lack of resources that prevented them from outproducing the western allies in the long term also prevented them from being able to achieve their objectives in the east.

From the perspective of Hitler and OKW, whether a victory seemed possible depends on what year you're looking at it. In the leadup to WWII, some felt it was not possible to defeat the Western Allies in a head to head fight, and especially not if the USSR intervened in the same conflict. In the summer of 1940, the WM pulled off something of a miracle by thoroughly defeating the French army and BEF in a stunningly short time. After this was accomplished, there was a feeling that the Germans had already "won", and that British capitulation or a negotiated peace of some kind would be following shortly. When it became clear this was not going to happen, invasion preparations began for the amphibious invasion of the UK. The Battle of Britain denied the Germans air superiority and without that there was absolutely no hope of a successful invasion. In retrospect, this was one of the two primary failures that led to the eventual downfall of the Nazi state.

1941 saw more successes on the ground for the Germans, with short sharp campaigns in the Balkans taking out Yugoslavia and Greece, the latter to help out the Italians who had got themselves into something of a quagmire there. When Barbarossa kicked off, it was met with extreme success. You could not have asked for a more successful opening to a major operation, they destroyed massive soviet formations and captured hundreds of thousands of prisoners. However, as we now know, Barbarossa would slow down and fail to achieve it's objectives in time. The Soviet success in holding the Germans back was the second primary failure of the Germans.

Please note that I do not mention these failures to mean that they bungled it and could have done better - on the contrary in both cases it was victories achieved willfully by Germany's opponents. I mean it in the literal sense that the Germans failed to achieve their objectives. Even if they had not underestimated the resilience of the British in the sky and the Russians on land and their ability to replace losses faster than the Germans thought possible, it is not clear that the Germans could have done anything about it. A realistic appraisal of the capabilities of their opponents, if anything, would have encouraged them to not go to war in the first place.

I should probably mention up front the counterfactual about Germany not going to war with the USSR before defeating the UK. With the Naval blockade established by the UK, the USSR (via Molotov-Ribbentrop pact and trade deals negotiated thereafter) was supply very significant quantities of raw materials to the Germans. So why couldn't they just keep building up their air force, build up their navy, and take on the British with the help of the Italians and other Axis allies over a longer period of time? The answer to that is three fold.

Firstly, defeating the USSR is the long term objective of the Nazi leadership. If the Germans successfully invade the UK in, for example, 1942-43, they will be delaying the invasion of the USSR until 1943-1944. The Red Army was in shambles in 1939-1941, militarily speaking. It was in the middle of modernizing, and the officer corps was still recovering from the Stalinist purges. An invasion in '43 - '44 would mean an invasion against an even larger Red Army than already existed, a better equipped and better led Red Army.

Secondly, the aforementioned dependence on the USSR for resources made the Germans dangerously vulnerable to Stalin's whims. While the USSR was generous and forthcoming early on, this was Stalin trading for time. As the Red Army finishes re-equipping and modernizing, there is no guarantee that resources will continue to be forthcoming. The Germans were not getting the resources for free, they were trading samples of German military technology and machine tools, and as the Russians feel less vulnerable over time, the Soviets would begin demanding more for their resources. There is also the possibility that the Red Army will eventually join the war on the allied side if the Germans show signs of weakening. I say this not purely for reasons of speculation (and certainly not in the Vladimir Rezun style of suggesting that the Russians were actually directly planning to attack the Germans, as that has been broadly critiqued), but because such hypotheticals were things that the Germans needed to consider when deciding on their course of action.

The third thing is that there was no guarantee that by stalling and relying on Soviet trade, they would ever be able to defeat the British. The Kreigsmarine took losses when they invaded Norway, and were already dwarfed by the Home Fleet at peak strength. The Luftwaffe was larger than the RAF, but they lost the Battle of Britain fairly decisively. It was a battle of attrition, and the British were winning it, outproducing the Germans in terms of fighters and taking fewer losses of machines and pilots on account of their home field advantage. With American aid being forthcoming, the Germans would not have been likely to break the RAF in subsequent years, and with an eventual direct entry into the war, the Americans would then guarantee that no such thing would be possible. Their hope, then would be for an eventual negotiated end to hostilities. But the British did not want a German-dominated Europe, and to allow the Germans to keep their gains would be a huge defeat for the British, even if they kept all of their own territory in tact. I cannot say that such a thing would not eventually have been accepted if they themselves were unable to break the Germans without Soviet help (almost certainly the case), but I can say with certainty that this would mean that the Nazis had failed in their initial objective - to secure for Germany a large, self sufficient territory carved out of the Soviet heartland.

Hitler did not begin WWII to have it turn into a world war (what a statement right?). The intent was the destruction of Poland and the eventual invasion of the Soviet Union. His aims in the west were non-existent and as far as he was concerned, the British and the French could keep their vast overseas empires-unchallenged- so long as Germany was left as the continental power in Europe. As you know, this all did not happen, the reaction to his invasion of Poland was the British and French declaring war on Germany.

That being said, to really address your question, North Africa was not an intended theater for the Germans. The Africa Korps was borne out of the Italian bungling of that theater and Hitler felt the need to intervene to save Mussolini some face. North Africa in the larger context of the war is a somewhat irrelevant theater as the majority of the fighting took place on the Eastern front- 9 out of 10 German Soldiers died there. Could Hitler have won the war? Yes, however there are some generally accepted conclusions on how.

1. The invasion of the Soviet Union was delayed by six weeks, the Yugoslavs had overthrown their king. The German army had been sent in to restore the pro-Nazi government. This delay would have disastrous consequences later in 1941 as the German advance into the Soviet Union would stall because of bad weather. You could argue that this six week delay would cost the Germans the Eastern front because of the criticality of defeating the Red Army in 1941. Sure there were other tactical and strategic mistakes made along the way, but this six week delay was the biggest.

2. Don't declare war on the U.S.A. There is no concrete evidence he did this to force the Japanese hand into declaring war on the USSR, however there is some speculation. Others believe this may have served as cover for what was the Germanys first strategic defeat in the war (see point 1)

With all that said, even with the blunders in 1941, the German army remained a formidable fighting force well into 1944. The British army without American help simply would have been unable to defeat it in the west and the USSR would do so only by attrition. Total victory over the USSR can be defined in many ways here, if you mean a drive to the pacific, I would say no; the sheer size of Russia just doesn't permit that and they Germans would likely be fighting an insurgency till today.

OK, first I will try to address some of the premises you start off with.

El-Alamein was totally irrelevant to the major war effort, which was the war in the East. The Germans deployed 2 or 3 divisions towards the Afrika Korps, which was neither here nor there in the large scheme of things. Secondly, it's a mistaken belief to assume that Germany's goal was to capture strategical resources in order to force a surrender. Rather, the German strategy relied on destroying the RKKA in the field, the strategical resources would then logically follow.

As for ideology, Hitler's goal was to create an autarchy for a final show-down with the USA in the future. You can accuse him of many things but he knew which side history was on, and he correctly identified the USA as a world power very early on. His response to that was bizarre (not trade or peaceful co-existence) but something akin to a medieval empire building project.

So excluding peaceful options, Hitler sought a military expansion in the East to challenge the USA (in essence he wanted to acquire territories belonging to Poland and the USSR). That would provide the proverbial breadbasket and 'Lebensraum' for a new Germany.

The way to accomplish that was imagined to be with a quick, fast, total war. The USSR was thought by every observer to succumb quickly to a German onslaught. German plans counted with a quick war (six months maximum) after which both the Wehrmacht and the armaments industry would turn towards the West, for production of airplanes and naval forces for the expected U.S. entry into the war. In fact, munitions production was already starting to cease by the time Barbarossa was under way and plans for downsizing the Wehrmacht were advanced. Neither of that happened of course, instead Germany found itself locked in a two-front war and having to devote resources to both the industry, navy, air force and army. Something they never imagined that they would have to do.

So to answer your question in short, that depends. Once Germany failed to force an end to the war in the East in 1941 time was against them. Germany had not only grossly underestimated Soviet manpower, but more importantly they underestimated their ability to replace losses in the field. Towards 1943 the Germans were bleeding the East dry to man defences in the west, the industry, and looming invasions in Italy and North Africa. At that point it was only a matter of time, and quite frankly it's remarkable they held out as long as they did.

That depends on what you view his goals as being. Many historians ascribe to him motives that are probably false. The invasion of Benelux was a necessity (staging areas) if you were to defeat France. Likewise Norway was born out of a necessity to protect iron ore trade from Sweden. Hitler always wanted his expansion to be to the East (and I think Tooze is a particularly bad source in explaining this). So you are left with the classical question of ideology contra strategy.