Everytime i try to place items into the display case they fall on the floor. What am i doing wrong.. I also cant figure out how to place things on the book shelves. I am playing PC version, I know how to take things in and out of cabinets. Please help me. Thank you.

You should be able to hold x when looking at the object to 'grab' it, then you can press x again to put it down

Whichever your "grab" button is, put the item to the center of your screen (when it's out of your inventory), and then press and hold your grab button. Then move around to where you wan to place the object and release the grab button. Although, still trying to prop up objects to sit the way you want to can be tricky. Maybe someone with better knowledge on how to setup books onto book shelves can advise you. Only advice I might suggest is assigning your grab button to your middle mouse button under the controls option. I find that more intuitive.

The default is 'z' on the PC.

I find that using Telekinesis makes it much easier to put things like books in shelves. Although it does take some practise and patience