I haven't played him but my interpretations would be:
The Assassin may move past an enemy, ignoring pinning. Work out one attack as normal. If he stops next to monster and wishes to attack this skill may not be used. Similarly he may have to escape pinning first. Cannot cause death blows.
Q: I'm not sure I understand this ability. Well I get the first sentence but the rest of it confuses me.
You can move, attack, move. If you begin your turn in a pinned position then you have to escape pinning first, as normal. If you end your turn next to a monster then you can attack as normal (so this special rule is redundant).
When behind a creature you may trade all attacks for a single cutthroat attack. Roll a D6. On a 1-3 you are elbowed back and lay prone for one turn. On a 4-6 you cause D6 wounds per battle level ignoring armour.
Q: Can this skill be used in conjunction with the innate Assassinate ability?
I'd say no, since it's not explicit, but this one's less clear than the first.