The solutions to the clues are
Network latency (+6) = PING
Support (+14) = BACK
Rocky hill (-4) = TOR
Parasite (+6) = TICK
Monster in Japanese folklore (+10) = ONI
Email folder label (-10) = SENT
Sad or feathers (+16) = DOWN
Unit of music (+4) = BAR
Water source or street name (+7) = MAIN
Pelvic joint (+6) = HIP
Quiz (-11) = TEST
Long sentence (+8) = LIFE
In each case, the number of blanks is double the length of the clue answer. For each word, we can "double" it and shift one of the letters in the second half by the given amount to create a word that fits in the blanks. The resulting words are
PINGPONG
BACKPACK
TORPOR
TICKTOCK
ONIONS
SENTIENT
DOWNTOWN
BARBER
MAINTAIN
HIPHOP
TESTIEST
LIFELINE
The shifted letters spell out OPPOSITE TO IN, which is OUT. We can perform the same process with the final (+1) to arrive at the answer OUTPUT.