1) The SS was a large organization. Yes, they were the ones that rounded up Jews to be sent to concentration camps. However, and this is the important point, the SS that we're talking about is the Waffen-SS, which was the war-fighting SS. The Waffen-SS wasn't in charge of committing atrocities.
Incorrect.
The Waffen-SS originated from the Freikorps (the organized band of roaming thugs in the early 30s who were responsible for much of the violent suppression of political opponents). During the war the Waffen SS was tasked with the most brutal assignments in Nazi-occupied territories. While the Wehrmacht served mainly military purposes (though they're not without their share of brutality" it was the SS which was tasked with such things as rounding up Jews and political dissidents, punishing populations, gathering slave labour, cleansing areas for re-population by Germans, etc. For instance, SS-Totenkopf (Death's Head) was tasked with overseeing the concentration and death camps throughout the war.
Essentially, the SS was the NSDAP's personal military and as such carried out the party's personal, often non-military agenda. The SS was also declared a criminal organization post-war (whereas the Wehrmacht was not) because of the war crimes.
3) The good Waffen-SS divisions were the elite forces of the Wehrmacht in 1944. There were also divisions that fought just as well as the SS divisions - Panzer Lehr on the western front, for example - but generally the SS divisions were considered the shock troops of the German armed forces as were used as such.
Only a handful of SS formations were considered "elite" (and then, mostly Germanic formations). Many SS units through to the end of the war were not seen in this way and received 2nd-hand equipment.
4) Since the Waffen-SS were considered elite, they received better equipment, were supplied better and more consistently, and had the first pick of recruits. This explains much of why they fought better in general. Personally, I feel that it has more to do with these factors, and with the pride and espirit de corps associated with being in an elite unit, than with any "indoctrination in Nazi ideology" factors. Somehow, I just can't accept the argument that being indoctrinated in Nazi ideology makes one a superior soldier - that sounds like just the sort of thing a Nazi would believe.
In one of the many ironic twists of the war, by 1945 60% of the SS was composed of foreign volunteers and conscripts, ie former slave labourers who vowed to fight on the battlefield rather than starve to death in concentration camps, as well as varied other nationalities who volunteered for one reason or another (ie, Indian nationalists who volunteered in order to fight the British Empire and drive it out of India). Even Jews attempted to join and/or ally with the SS and the NSDAP in order to fight the British who at the time controlled Palestine - they were, however, uninformed about the policy of extermination of their race, and were rejected.
Most of what made the SS "elite" (those formations that were elite, that is)
was their dedication to the Reich. Overall they received only slightly more training than regular Wehrmacht soldiers (and this training was constantly reduced as the war dragged on and the need for more soldiers became overwhelming). The SS-Hitlerjugend, for instance, was composed entirely of children. Children aren't very good soldiers (atleast they weren't back then before the popularity of video games) but were feared combatants because of their
incredibly overzealous determination and absolute brutality in combat. Whereas more ordinary soldiers of the regular military would usually (but not always) not hesitate to surrender when faced with incredible odds, SS troops would routinely fight until the bitter end, charged with the knowledge that they were fighting for their Fuhrer.
Anyway, it's neither here nor there. There were Wehrmacht units who are far more deserving of the "elite" title (Panzer Lehr like you said, Grossdeutschland) and when it came to actual battle statistics, from what I've mostly seen, the most "elite" formations in the German military were the Fallschirmjaeger, Luftwaffe Paratroop units reverted to a more traditional infantry role. These were really the cream of the crop and particularly in Italy they proved themselves perhaps the best conventional forces in the world. So if there was to be German elites it would be them, not the SS (though the SS are probably more symbolic)
In either case we've deemed German elites unecessary. Germany's "eliteness" will be its ability to build large bunker fortifications. And if you want "elite German combat units" then you're just going to have to play better, and then you'll be "elite" :)
