I'm still kind of unsure about Apollon but I'll definitely try and watch Medaka.
A good mystery to me is one that is both surprising and satisfying. Even if it ends up being something like a husband killing his wife, I want to be surprised that it was him (because he seemed innocent) and satisfied knowing his dark side came to light. When a mystery isn't surprising half the fun is gone, really. Columbo is great because it actually flips the murder mystery formula on its head: You know who did it within the first five minutes of the show, the rest of it is about how the murderer tries and fails to get away with it.
I'd recommend Neuro in a heartbeat, but its not really a mystery manga. I mean, it has tons of mysteries that the hero and heroine solve, but its more about Neuro's relationship with humans, with a bunch of sadism thrown in.
I'm not sure if I have the channel its going to air on.

But if its on I'll totally watch it!
Cricket is the most popular sport in Pakistan, and in its original British raj form its quite boring. A single match can last 3 days. But the ICC have updated the sport to have One Day Internationals (4~5 hrs) as well as Twenty-20s (1.5 to 2 hours). I find cricket interesting because when you are up to bat you aren't acting alone - you have a batting partner. Also, the way players get out is more interesting than in baseball, personally.
I'm not sure if I can answer this properly.

Probably both and neither. I'm not sure how religious I am at all!
Oh awesome, I liked history as well in high school!

My favorite historical things to learn about at the moment have got to be Kuwaiti history, as well as the history of the Arab peninsular, pre-Islam. What are your favorite time periods in history, Niichan?