1. What do the following words have in common?

COVE
CROW
YEAR

2. What do the following words have in common?

ARSON
CHAR
ERRANT
ITCH
TESLA

3. What do the letter pairs have in common?

HA
CO
MA
WO
GI
RA
LI

Answers:

1. Each word can be followed by N to make a new word:

COVEN
CROWN
YEARN

2. The first two letters of each word can become the last two letters and still have a valid word. 

ARSON - SONAR
CHAR - ARCH
ERRANT = RANTER
ITCH - CHIT
TESLA - SLATE 

3. Each letter pair becomes a word with the addition of the letters VEN:

HAVEN
COVEN
MAVEN
WOVEN
GIVEN
RAVEN
LIVEN