It's called a locker hook and is used for weaving, not crochet. But it sure does look like a crochet hook.

that would be a size P crochet hook

It's exactly how it sounds. After starting the next row, put your hook in the chain of the next single crochet stitch, yarn over the hook and draw the hook through the loops.

If you're still stuck there are some good instructional videos on you tube.

In crochet terms, a speed hook is just a name given to a very large crochet hook. These types of hooks are often used when crocheting rag rugs or large handbags.

It looks like a knitting needle with a crochet hook end instead of a point. It's used for what's called tunisian, afghan or interweave crochet.