These refer to call-outs/game quotes from The Addams Family pinball machine, the best-selling pinball machine of all time. Once you get the aha, there is a convenient list of all the game quotes on Wikipedia, which we updated for the sake of ensuring all the relevant quotes from this puzzle were there.
The clues about “my dad” refer to phrases spoken by Gomez Addams (voiced by Raul Julia), while the clues about “my mom” refer to the smaller number of phrases spoken by Morticia Addams (voiced by Anjelica Huston). (The clues are most likely written from the perspective of Wednesday Addams, although they don’t correspond to plot points of either the pinball game or other Addams Family media.)
My dad liked to take us all to the beach, but he didn’t tend to go into the water himself. → Have a nice swim!
I once asked a friend where the Stargate SG-1 series had originally run. My friend thought it was Syfy, which my dad wasn’t very happy about… → SHOWTIME!
My dad once produced a feature film, but apparently it was never released in any format and was instead placed immediately in the movie studio’s back catalogue! → Straight to the vault!
My dad had a brief stint doing tech support, but he got pretty irritated when callers forgot to try the most basic steps before calling him. → It’s not plugged in yet!
Our family’s doorbell was often broken, so my dad told visitors what to do when they arrived. → Knock three times!
My dad tried to get everyone to join him for some genealogical field research. → Out to the cemetery! Come on, everybody!
My dad went to see Steve Martin perform back in the 1970s and told Martin how hilarious he was. → Heh heh heh, you’re a funny guy…
One time my dad was in medieval Iceland and wanted to express his gratitude to the governmental assembly (although I have my doubts as to whether they could understand him!). → Why thank you, Thing!
We were eating together in a restaurant and I asked for a doggie bag; when the waiter demurred, my dad started arguing with him about the basis for this policy. → Who says you can’t take it with you?
My mom never suffered fools gladly. → You should know better.
My dad could easily identify cocktails that contained hard liquor from those that didn’t. → That’s the spirit!
My dad hired a governess for a young Jerry Garcia and Bob Weir and explained to her what her job consisted of. → Raise the [D]ead!
My dad was a big fan of Ayn Rand, and would usually credit people’s accomplishments to their following her advice. → There, see what greed will get you?
My mom often discouraged friends from masochistic practices. → Don’t torture yourself.
My dad would send fan letters to Bob Barker in the early twenty-first century telling him how great The Price is Right was. → Good show, old man!
My mom was very hospitable to visitors—though maybe a little too formal about it. → Welcome, honored guest.
My dad took us all out driving in a souped-up sports car and was always bragging about its acceleration and its amazing V8 engine. → Feel the power.
My dad was always super-busy and would reject everyone’s invitations. → No time for that now!
The indices then extract the following letters from these answers:
N 6 HAVEANICESWIM
O 3 SHOWTIME
V 14 STRAIGHTTOTHEVAULT
I 1 ITSNOTPLUGGEDINYET
C 4 KNOCKTHREETIMES
E 8 OUTTOTHECEMETERYCOMEONEVERYBODY
H 1 HEHHEHHEHYOUREAFUNNYGUY
A 6 WHYTHANKYOUTHING
C 11 WHOSAYSYOUCANTTAKEITWITHYOU
K 10 YOUSHOULDKNOWBETTER
E 8 THATSTHESPIRIT
R 1 RAISETHEDEAD
I 19 THERESEEWHATGREEDWILLGETYOU
N 3 DONTTORTUREYOURSELF
S 5 GOODSHOWOLDMAN
U 16 WELCOMEHONOREDGUEST
L 4 FEELTHEPOWER
T 3 NOTIMEFORTHATNOW
NOVICE HACKER INSULT is the extracted phrase, which is a clue for the answer SCRIPT KIDDIE.