First of all it should always be noted that the Waffen SS was very diverse in regards to quality. The first Divisions had outstanding quality, these quality declined with later stages of the war. Later SS divisions were filled with foreign conscripts with low requirements opposed to the all german divisions with lower numbers. When people ask questions like yours i assume they want to know about the single digit Divisions which are well known.
To get accepted into training for the LSSAH for example the requirments were very tough.
The combat training was pretty much the same like Wehrmacht soldiers but they had more political classes.
Yes often. That was the point of the Waffen SS. Many of the soldiers serving in the single digit SS Divisions were Nazis. The list of war crimes commit by SS units is a further clue.
Don't know. This asks for generalisation. I guess you are safe to assume that soldiers in the first SS Divisions "looked down" a bit on regular soldiers. They were meant to be the definition of the "master race". Their combat record also was oustanding so i guess they felt kinda special. The opinion of normal soldiers likely differt maybe depending on their general stance on NAZI ideology.
why were they needed
Well, they were not. They served no special purpose. The administration of these troops soacked up extra ressources.
First there was only a small SS unit which was directly planed by Hitler. The Leibstandarte. This was the personal guard unit for the Führer. Later the number of SS units increased. At the beginning the idea was to create units which were complete loyal to Hitler himself later people like Himmler expanded the Waffen SS to increase their influence in the Reich. To be frank, the concept was big nonsense.