1. What is unusual about the first six letters of the alphabet - ABCDEFG?

Answer:

ABC can be anagrammed into CAB. DEF can be anagrammed into FED. No other  consecutive three letters in the alphabet have this property. 

2. Only one set of four consecutive letters of the alphabet can be anagrammed into a common four-letter word. What is it?

HINT:

It starts with a letter that is in the second half of the alphabet.

 

Answer:

 

RSTU - RUST or RUTS

 

Credit:
Martin Gardner

Colossal Book of Word Play

2: (Thanks to Murray W. Pearce)