1. The same word can both precede and follow each word below. What is it?

ALL
RUN
TAKE
HANG
SLEEP

2.  The same word can be inserted into the name and words below to make new words. What is the word to be inserted and what are the new words?

MEN
CON
CEL
TAR
HEY
PING
DING
CHER
STING

Answers:

1. OVER

2. The word to be inserted is ART:

MARTEN
CARTON
CARTEL
TARTAR
HEARTY
PARTING
DARTING
CHARTER
STARTING

Credits:
#1: John Underwooed
       FRONT AND BACK

#2: Patrick Jordan
      ARS GRATIA ARTIS