HTC Explorer wallpaper display problem
some portion from all the four sides of the cropped image is not displayed.


At least it seems so -- but that's perfectly normal ("works as designed"). Android does not think of it as a background image solely for the "recent homescreen", but rather for your "collection of homescreen pages". If you swipe through your homescreens left-to-right (or in the opposite direction), and watch the background image while doing so, you will notice it slightly sliding along. So the "left side" of your background image aligns with the left-most "page", while the "right side" does the same with the right-most page.


  the phone has 320x480 screen resolution, I have a wallpaper from net with the same resolution, but the phone still asks me to crop it


The reason for this hopefully became clear with above explanation. So generally spoken, you will need a picture with the actual height of your screen, but being wider than the actual screen width.