What makes a bomber able to deliver nuclear bombs? Currently the German Luftwaffe has Panavia Tornados to deliver American nuclear bombs in case of war. The bombers are getting older and are currently modernized. The German Luftwaffe also has Eurofighter Typhoons which are said to not be able to deliver nuclear weapons. Why is that so? (Same goes for the F-35 and the F-22)

AFAIK all that's needed for an aircraft to deliver nuclear bombs is


The ability to actually carry the bombs, which probably conform to some standard "form factor".
Some special electronics for arming the bombs, which must be installed into the bomber - this probably also follows some standards.


Is that all? I seem to remember some special aerobatic maneuver the aircraft should be able to perform to allow the survival of the crew. Does that exist and is it a problem for modern fighter/bomber aircraft?
You are right in saying that's all that's needed, with the addition of a strategic or tactical need.  

The need for a "special evasion" technique is only needed for aircraft dropping megaton range weapons in an air burst.  Kiloton range weapons could be dropped from altitude with no special evasion required except a lot of speed.  Sub-sonic aircraft would need to be "frisky" in their escape. Read about Tsar Bomba for a good example which demonstrates that even with the biggest bomb ever dropped, a relatively slow, lumbering aircraft can escape.

Even helicopters can drop nukes.

Most aircraft are only tasked to drop tactical, low yield weapons.  The real madness is assigned to subs and missiles.

As the comment above says, I suspect that most crews dropping strategic weapons will not care much whether they survive or not.