The rules say you get a free spin after an opposing figure ends its movement in an ajacent square.

Say an opposing figure moves into my rear arc to attack, do I get the free spin before the attack (because the opposing figure ended its movement), or after the attack (because attacks are considered part of movement)?

Before, because that is the entire point of the free spin. You can face your attacker so he/she/it won´t get any rear arc bonuses and you can fight back.

It that case, it seems it is almost impossible to melee attack someone from their rear arc. They would have had to intentionally left their back turned to an enemy standing right next to them. I guess this makes the rear arcs only used when surrounded by enemies.

If somone has sneak attack though no free spin is given. So if a MS with sneak attack moves into your heroes rear arc then youfr hero takes the penalty for the rear arc attack plus the double damage from sneak attack.

You almost always have to get at least 2 figures on opposing sides of an enemy figure to get a rear arc attack.