So when our coin sits at Bittrex, is Bittrex collecting a stake on those coins?
Probably. Bittrex is known for doing anything to make a buck. They even go as far as getting insider information from devs and running bots on their own site to accumulate cheap coins.
Wouldn't put that as a possible procedure at some exchanges, but there's no evidence that Bittrex is or isn't doing that. There needs to be regulations on some things in cryptos. Imagine if the stock market didn't have some form of regulations, the elite would certainly price fix and manipulate the market to there favor completely.