can you shoot a .22lr out of a .22 magnum cylinder? i allready know you cant shoot a .22 mag out of a .22lr cylinder.

yup.

No.  This isn't like .38sp/.357 or .44sp/.44mag.

The gun won't blow but much of the time the case will tend to split/rupture which blows all sorts of debirs every which way.
I would expect accuracy and power will be degraded (not that a mini derringer has a whole lot of either in the first place)
I seem to remember one of the derringers haveing both cylinders but I don't know if it was a charter arms or the NAA

Absolutely not!  Get the 22 cylinder made for the black widow to shoot 22 out of the 22magnum frame and yes, accuracy if you get any with such a short barrel will be null and void.  A belly gun at best.

barrel length is irrelevant with regard to inherent accuracy. The overall size of these guns makes them nearly impossible for a person to actually see what they will do––and on the point a the lack of accuracy created by that situation, I will agree with you. I can't shoot my 1 7/8" worth a damn due to the size of the thing. It's impossible to hold it in a manner that allows use of the sights while maintaining a decent grip.



With a two shot derringer that dad owns, I can regularly hit spent 12 gauge hulls at ten to fifteen paces with the top barrel. I never figured out the proper sight alignment to hit with the bottom. I do pretty well to hit a paper plate at the same distance with my NAA because it's just so difficult to hold.



 

The Black Widow is a completely different from the ‘pocket’ guns…

Link

They come in 2” or 4” barrels with either Fixed or Adjustable sights

A new contender is  The Earl

All are available as .22 Mag with an option for .22LR cylinder.

If you get the folding grip for the NAA revolvers, then you can have a normal grip.