Suggested answer:
(1) Yes, the simile sleep like a log occurs once in the corpus:
The nights in Denver are cool, and I slept like a log.
(2) Other similes including sleep like that occur in the corpus are:
He'll sleep like a baby.
She might even sleep like a brick...
He noted a female bum drunkenly sleeping like a dugong...
Sunday she slept like a stick.
(3) A simile is an expression / a figure of speech that contains a comparison that is spelled out in a phrase beginning with either like or as. Examples from the corpus:
Polly, light-footed and sharp as a needle in grasping the rhythm...
You eat like a pig and look like a rake.
Read about similes