Question

Does reversing the order of digits of a 2 digit prime number always result in a prime number

Answer 1

No 
for example:
     
                29   if you switch the digits it becomes 92 and 92 is composite because 2x46=92

Answer 2

No, for example, if you had the prime number 23, and you switched the numbers around, it is 32. 32 is not a prime number.