1. Well, the minutes must be palindromes...
Hours range from 00 to 23. All but 16,17,18,19, 06,07,08,09 have palindromes in seconds.
24-8 leaves 16 times that hrs/secs will palindrome. For each of those 16 times, there are exactly 6 times that the minutes will palindrome also.
So for 96 seconds (16*6) out of the day, or 1 minute, 36 seconds, Ivan will be happy.
2. The words in each sentence are in alphabetical order.
3. Paladin decided to kill two birds with one stone here. Rather than make a sign and display the clocks, he made the clocks into the sign. The clocks were set so that the Minotaurs on the faces of the clocks spelled "GREY LABYRINTH" in semaphore (the international flag signalling system) as accurately as possible. After the conference, the Minotaurs spelled "GREY L BYRINT". At a glance, Paladin knew that two clocks had been taken, the "A" and the "H".
4. The corner balls get counted twice, the center balls six times, and the others four times. The highest total can be achieved by placing 1, 2, and 3 at the corners, and 15, 13, and 11 in the middle. The rest can be arranged so that consecutive balls aren't touching. Total, 546.
5. A leech. When you don't want it, it takes your blood. Bad luck for the leech if you see it before it drinks it fill, because it just asking to be burned off with a cigarette. There was a time when leeches were used to bleed patients, to prevent blood poisoning or reduce swelling (they take the blood you don't need). However, there are better methods than leeching these days; but if you're in a primitive society, or desperate enough, you might have to put up with it.