How many blocks do I need?

Exactly 1.125 for standard nominal 8 × 16 inch CMU — the actual block is 7⅝ × 15⅝ inches and the ⅜ inch joint brings it back to a clean 8 × 16 module. So a 320 ft² wall takes 360 blocks before waste. In metric markets a 390 × 190 mm block with a 10 mm joint gives 12.5 per square metre.

Because the nominal size includes the mortar joint. That is deliberate: it makes the coursing arithmetic work out in whole modules, so a wall built to nominal dimensions lands on block sizes without cutting.

In everyday use the terms are interchangeable, though strictly a cinder block used cinder aggregate and is lighter and weaker than a modern concrete masonry unit. What you buy today is a CMU, and it is graded by strength and density rather than by that old name.

No. This is the block count only. Reinforcement, grouted cells, bond beams and lintels are engineered elements that depend on the wall height, the loads and local requirements — take them from the drawings rather than from a block count.