BeagleBone Black I/O

Can use its digital I/O to control the Motor Derive H-Bridge which takes 5V as input?
Can I interface Optical encoder with Digital pins - Optical encoder gives 0V or 5V ?
Can I interface sensors which I used to interface with micro-controller?

The board is 3.3V output only. It may be able to drive certain devices but you run the risk if protection diodes or internal pullups that could cause the pin to go to 5V, damaging the processor. I would level shift the signal from 3.3V to 5V.