How to share and project Powerpoint presentation with ARD
In answer to the first query - When the students connect they should see both of your displays and then be able to select Display 1 or Display 2 for a closer look at either one. These options appear (or not) depending on the display arrangement setup under Displays in System Preferences.

The bottom line is, ARD is not really suited to this task. There is a piece of software that does exactly what you're after, but it does cost. It's called LANSchool. 

The killer LANSchool feature that you're looking for is - 'Show Teacher's Screen'. This overlays your screen onto a selection of student machines. There's a 30 day trial available, I highly recommend you try it out!