Well, they might be losing money in fees but if they are involved in some sort of scheme to buy/sell before anyone else, I'm sure they would make a lot more money. If it's not on purpose, then it's a shit exchange that hasn't been able to solve this issue in 3+ years.
That is conceivable. I'd be dead surprised if Bitmex and Bitfinex weren't doing something like that. Coinbase though has some prestigious investors and if that were ever proven that wouldn't do their rep much good just as they're trying to position themselves as a legitimate player in finance.
There was the Coinbase BCH launch to draw on which was an absolute shitshow. Luckily Coinbase conducted an 'internal investigation' and surprisingly found that that no wrongs had occurred.
I've no idea of the strains heavy movement makes on exchanges but it's not an easy thing to deal with. Kraken did it constantly for years until they completely rebuilt their back end if I remember rightly.