(In reply to
answer by K Sengupta)
The word "share" is common to each of the items as described in the puzzle. To visualise the reason, observe that the words which are the correct responses to each of the foregoing queries, are the anagram of the word "share", when precisely one letter is obviated from them.
Hence, we observe that:
(a) In LINE 1
Santa's friend -> Dasher -> Dasher - D -> asher -> share
(b) In LINE 2
Deceased inside -> Hearse -> Harse -> share
(c) In LINE 3
In a deck(of cards) -> Hearts -> Hears -> share
(d) In LINE 4
Potato preparer -> Masher -> asher -> share
(e) In LINE 5
Look through -> Search -> Searh -> share
(f) In LINE 6
Hair remover -> Shaver -> Shaer ->share
(g) In LINE 7
Hair remover -> Shaver -> Shaer ->share
(h) In LINE 8
Wool remover -> Shears -> Shear (or, hears) -> share