Which Schecter 7 string is the most popular?

The most popular overall is the Demon 7 FR model in Crimson Red Burst.

What type of pickups do Schecter use on their Demon 7 guitar?

Schecter use their own design HB-105S pickups. These are active units and are particularly good at producing high gain sounds with low levels of background hiss.

What is the Schecter 'Diamond Series'?

Diamond Series is essentially every Schecter guitar that is not a US-made guitar. The Series started in the late 90s as a term to differentiate the imported guitars from the American guitars. These days, the majority of Schecter guitars sold are Diamond Series models.