Long story short, I was wrong to categorize martial adept abilities as "per encounter"?
Only when you gain a maneuver by a feat it becomes per encounter, correct?
Martial study is complex. If you use it to acquire a manoeuvre when you don't have an initiator class then yes; however if you have levels in an initiator class then no.
π = 4
Consider a 5' radius blast: this affects 4 squares which have a circumference of 40' — Actually it's worse than that.