Is there a place in Stack Exchange where you can share an excerpt of a story or proposed book and receive feedback?
No, there's currently no site (or other formal process) where you can get critiques on Stack Exchange. The closest I know of is the mid-week group chat at writers where we freewrite and discuss, but that's not on the main site.
This site has decided that critique questions are off-topic, because they're very difficult to make work within a Q&A framework; we tried them and only later decided against having critiques here.
You're not the first to ask about this, and it seems other people are also having problems getting critiques to work on Stack Exchange. There was a critique site proposal at area 51 (our site for creating new Stack Exchange sites) but it didn't take off.