You need to perform ten Overdrives successfully, meaning that you have pressed the X Button when the cursor is at the center of the meter.
Tidus' ODs don't need to be successful to count.

You need to perform 25 successful Overdrives to acquire Energy Rain
30, not 25.

Spin the right analog stick clockwise to get the highest number possible.
It needn't be clockwise. Both directions work.

The number indicated is also the number of time you need to do full rotation of the stick in order to get the number go up by one.
False. The number of spins required depends on the spell used and Lulu's Magic stat.