Dungeon Lords Questions - Really Hard!
I worked through the seven questions myself when I first bought them game, but as I don't remember the answers right off the top of my head, I'll preface this answer with the statement that I've gotten the following answers off of a thread BoardGameGeek.

Question 1: If you have to gain more evil than evilometer allows you, you are not gaining any. Can this theoretically happen in the second round of the game?

On round 1 and 2 you play food, getting on the third space (in round one two people do it before your first placement). Thats 4 evil.

On round 2 title envy event occurs. You collect 1 evil per title, for the following: 
Most evil (from your 4 evil from food)
Most room (1 vs 0/0/0)
Most tunnels (You dug 2, no one else dug, 4/3/3/3 after the room)
Most monsters (1 vs 0/0/0)
Most imps (4 vs 0/0/0)
Most resources (you gained off the food, they spent some if needed).

Note that you cannot collect 'fewest conquered tiles'.

Thats 10 evil, maxing you out, but we still need one more, so your Monster that you recruited is a Witch for one evil. (Vampire not needed. Ghost doesnt count as a monster for monsterlord). 

Your three actions each round combine to these 6 actions:
Food, Food, Tunnel, Imps, Monster, Room.

We go above the top of the evilometer on Title Envy when the final title is awarded. (Note: that Witch recruit was before the title payout, so yes it works).

Question 2: What is the theoretical maximum number of imps a player can accumulate during a 4 player game?

30
3 from the beginning of the game, 12 from magic room (4 x 1 in first year, 4 x 2 in second year), 15 from actions (the player have to take imps as first action each round except last round, so he will be at least once first and so obtain only one imp 7 x 2 + 1 x 1).

Question 3: What is the highest possible damage one trap can deal?

Nine. Poisonous food used onto eight life adventurer with one extra life because of magic food.

Question 4: Can it happen that an illusionary hero created by Second Year’s Illusion spell survives a combat round?

Theoretically, it can survive even a round in which was party conquering.
1st round – illusion is created. Party doesn’t conquer.
2nd round – illusion is boosted by magic food. Party doesn’t conquer.
3rd round – illusion survives one fatigue from conquering.

Question 5 What is the theoretical maximum number of actually healed damage in a single round of combat if there is no paladin involved?

Ten. Party composed from two priests with three hearts each and one wizard (three casting symbols). Initially an illusionary hero with two wounds is created (analogical to previous answer) in first two rounds. Also some damage is dealt among the adventures. In the third round slime hits the party, the wizard casts healing spell and one wound is healed to each member of the party including the illusionary hero. Two priests heal the rest six wounds.

Question 6 What is the lowest possible score you can achieve in the game?

-72. You can have sixteen tunnels which results in 8 x -3 points each year for unpaid taxes. Nine tunnels were destroyed by adventures 9 x -2 (once double conquering because of the spell) and the visiting minister of Dungeons was hungry (2 x -3).
Summary: -48 (unpaid taxes) -18 (destroyed tunnels) – 6 (visiting minister) = -72

Question 7 It is start of the last round of a 2 player game (fall of Second Year) and opponent has no production room. If scored now, you would win all 7 exclusive titles. May it happen you score no title (exclusive nor shared) at the end of the game?

Yes, even if your opponent does not perform one of his minion actions.

First player has all titles, second has none.
Second player dig four tunnels as his first action and hire monster as second action. First player’s actions are chosen so that they do not interfere with loosing titles.
Special event is an Earthquake. First player looses two rooms, second player looses two tunnels (Other option is the Extra tax special event).
The Lord of Dark Deeds – lost in the combat (because of destroyed tiles)
The Lord of Halls – lost because of an Earthquake
The Tunnellord – lost by the only minion action of the second player
The Monsterlord – lost in the combat (because of Dimensional gate)
The Lord of Imps – lost in the combat (two or three Kamikadze Ims)
The Lord of Riches – lost in the combat (two or more traps used)
The Battlelord – lost in the combat (because of destroyed tiles)
Second player doesn’t loose any tile or monster in the combat and he uses no traps (For example party of a paladin and three rogues (the case the first player has taken action Improve Reputation so the second player is the most evil from the beginning of the combat), first round a daemon and a dragon in the Anti-magic Room, second round a goblin finishes the three wounded rogues in Training Room).