I am not any sort of doll expert, but it seems to me that basic display methods should be similar to any other fragile object. Wide shelves for stability, breakfront glass if you have it, and light dusting every week (more if you are in a dusty area of the country).
For the dolls in particular, I suggest cork-board either as the floor or back wall. The reason is that you can fix the dolls to it quite invisibly with twist-ties and flat topped push-pins; loop a twist-tie around a foot, fix in back with a pin, and hide it either by choosing a similar color to blend or hiding it under a fold of cloth. You should be able to modify this technique to pose or adjust the dolls in virtually any position.
Another thing you might do is pose them with props; anything they can rest a limb on, or sit on, will help with keeping the display natural. You don't want the artificial waxwork look here! I don't know how much space you have, but a small vignette for each doll would be fun to create, and you could redo it every other month for variety. (Again, I might be over-thinking this ;)
Hope this helps! #2 has a handle on your specific questions; you can't go wrong with a good ironing!