1. The same two letters, in the same order, will change each word below into a new one:

WE
EVE
TEN
PER

2. The same two letters, in the same order, will change each word below into a new one:

HAT
POD
LACY
SLIGHT
DATING

Answers:

1. The letters OK can be inserted into each word to form a new one:

WOKE
EVOKE
TOKEN
POKER

2. The letters UN can be inserted into each word to form a new one:

HAUNT
POUND
LUNACY
SUNLIGHT
DAUNTING

Credit: Both puzzles
LA Times Crossword
Sylvia Bursztyn and Barry Tunick
#1: IMPLICIT APPROVAL  
#2: UN INTERVENTION