Smallest screen size without issues like scaling
Using the Screen size calculator, choosing 16:9 as the aspect ratio, and entering 2.5 inches as the diagonal give the result:

Width: 5.5 cm / 2.2 inches
Height: 3.1 cm / 1.2 inches



  Also how small do you think apps can support before problems occur ?


It depends on whether the apps' developers have coded them to Support different screen sizes or not. If they have not, then going below 2.5 inches will become problematic.