Here, let's group all of the silly mentor quotes and the way to get them during the game. If you do new discoveries or know how to get some of them, please share the info with us so that I'd bring the changes. Thanks for future contributions!
Unknown
Unsure
Confirmed
"Hmm. Are you sure you haven't been playing Populous?" = Unknown
"Keeper, your dungeon is emptier than your head" = Have your dungeon with less than 5 creatures (Imps not included) for 50 game minutes
"Trick or treat, Keeper? Buwa ha ha!" = At Halloween at 6:06 PM and midnight
"You’re taking your time on this one, Keeper. Scared?" = Unknown
"Do you await some ominous sign or portent from the Undergods of Fire and Soil?" = Unknown (but is surely related with the Temple)
"The very rock yawns with anticipation of your next fascinating move" = No user input for 160 real seconds
"Familiarity breeds contempt, Keeper" = Unknown
"It is the Witching Hour. Curses are half-price" = At midnight
"Surely, even Dungeon Keepers must retire to a Lair of some description?" = At 1:00 AM
"Hello? Are you still there? The Imps are about to lock up" = At 2:00 AM
"Your nocturnal perseverance has earned you a hidden gaming tip. GO TO BED!" = At 3:15 AM
"You know that low, broad, downy-soft item of furniture in the next room? It has the power to cure fatigue and restore vitality" = At 3:00 AM
"You’ll go blind, you know" = No user input for 160 real seconds over a Torture Chamber filled with 5 or more Mistresses being tortured
"You have an excess of Mistresses. There’s a word for Keepers like you" = Once you have attracted your 10th Mistress from (one of) your Portal(s)
"Hic! Your creatures demand cakesh and fine winesh" = Unknown (but is surely related with the Casino)
"A lost soul has entered your dungeon. Oh – no, it’s wandered out again" = At random every 40 game minutes
"A neutral creature sends word that he can’t make it today" = At random every 40 game minutes
"Your dungeon floor is lumpy. Order your minions to jump up and down" = At random every 40 game minutes
"Hungry Demons cannot reach their toes" = At random every 40 game minutes
"The Wizard needs food" = Unknown
"Your dungeon is on an incline. Angry creatures cannot play marbles" = At random every 40 game minutes
"Big monsters! Big prizes! I love it!" = At random every 40 game minutes
"Your dungeon is full of yoghurt" = At random every 40 game minutes
"Keeper, you have something unpleasant under your fingernail" = At random every 40 game minutes
"Micro-piglets stalk your dungeon. Beware!" = At random every 40 game minutes
"Your dungeon is damp. Install central heating" = At random every 40 game minutes
"Never eat anything bigger than your own head, Keeper" = At random every 40 game minutes
"Your Lair has been re-carpeted" = At random every 40 game minutes (it doesn't even require a Lair)
"Your minions demand cable" = At random every 40 game minutes
"Timing is... ... ...everything" = At random every 40 game minutes
"If you were any kind of a real keeper you would have won by now" = After 120 game minutes (2 game hours)
"Other Keepers never forget their minions birthdays" = Unknown
"One of your imps does a great impression of you. He can even do the ears" = Once you have created your 20th Imp from the Create Imp spell
"It's party night!" = Involves to have some creatures gambling in the Casino during night time (requires further testing)
"Let's party like it's 1999!" = At 0:58 AM every Saturday (Thanks nijuni_kuro!)