halacha theory - Can a man who has undergone sex change give his wife a Get?

If a married Jewish man undergoes the hormonal and surgical procedure of sex change, and "he's become a woman".

1. 
   

   Would he still have the Halachic status of a man, at least relating to his marital status?

   
   


2. 
   

   Could he give his wife a Get if he wanted to?

   
   


3. 
   

   Would he be deemed by Halachah as mentally competent to give the Get?