This question is dedicated to Parbatya, the Guniess who is always there with a correct answer for my pirated mathematical problems.

Parbatya's special mobile number has ten digits, beginning with 0.
 
When I tap it into my phone keypad, I note that-
- no two adjacent digits of his number are in the same column or row of my keypad
- the 2nd digit is even
- the 4th digit is odd, and 7 different from the 3rd digit
- the 5th and 6th digits differ by 1 
- the last 3 digits are in ascending order

My keypad is laid out as shown:

123
456
789
*0#

What is his number?