Can I use arduino and mobile phone screen to make a touch board?
First, find a suitable phone screen! Good luck. Most of the touch screens that I have found are resistive, and will never feel like an iPhone. Try googling "Arduino touch screen". Adafruit have a promising one.

Once you find your screen, you will need to interface to it. With luck it will come with a pre-built library. Otherwise you will be up for quite a lot of coding.