Yes, all true Holger. But we must remember the SS of the mid-30's was a relatively small group and its role(s) greatly expanded until the end of the war.
In that growth I think the SS becomes quite a blurred 'organization'. For instance, many party officials would have been considered SS, especially those in the Interior Ministry, Security/Police, and other institutions. Though these people would be considered SS, they were not Waffen SS; which was distinctly military.
As for the SS units that were in Berlin, I believe there are several reasons to explain the ferocity of their resistance.
To be clear, there were few Waffen SS units in Berlin. In fact, there were three cohesive 'units', and I use that liberally, of the Waffen SS in Berlin - those being; elements of the 11th SS, and two guard battalions of the 1st SS.
The majority of SS in Berlin were the party functionaries and institutional personnel who happened to don a SS uniform; many, without a doubt, staunch Nazis who fought to the death.
That, coupled with that fact that the Soviets didn't make distinctions and were not particularly keen on taking any SS-man prisoner, made it a simple choice of life/death struggle.
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