There was an SEC study done about 15 or so years ago. I'll look for it and post a link. There also used to be a national exchange rule which as I remember it - required your quotes posted on a national exchange to reflects your dark pool quoting. I'll do some homework, but if that is active I would expect none of the major MMs to be there except on days of corporate actions.
Even for market makers, you need a healthy level of trading activity. Traders hitting the buy and sell queues allowing you to earn the spread. In some markets, activity during ETH could dry up to the extent that there are only a few trades every few mins. That actually makes market making dangerous since you can't offset your positions quickly.
Yes, it is. Low liquidity after hours allows MM's to price gouge everyone. OTC doesn't have market hours. If a MM enters a position they can hedge within 5 minutes OTC with price locked in at what they've traded at. Swaps & Forwards are what they hedge with, and there counter parties don't exactly try to make money off of them.