I'll try to address the individual points:
Has flying become so automated that the crew is handed a flight plan and sent on their way without knowing where they are going.
No. We always know where we are going before we get to work. I know my schedule the month prior. Even the reserve pilots (on-call pilots) know where they are going before they get to the airport. Besides, we have to double check the work of the dispatcher to make sure the flight plan is correct.
Don't think you can blame the flight crew for this one, they merely flew to where the flight plan told them to. The blame falls squarely on whoever filed the wrong flight plan.
There has to be some type of flight planning done by the flight crew.
In the airline world, almost none of the flight planning is done by the crew. The dispatcher handles that and much of that work is done by the software. We pilots just give the flight plan a "gross error check." Again, I know my scheduled destination before I get on the plane. If I'm scheduled to fly to 2,300 miles to SFO, but the flight plan shows our route is 1,000 miles, that would be a gross error.
I haven't personally filed a flight plan in at least 19 years.
I bet there was a gate change or aircraft change at the departure airport that got mixed up. I looked up who actually flew that flight. It was WDL Aviation, a German Charter airline, running the route for British Airways. From what I can tell, WDL is not a normal regional airline partner, but an actual charter company. Maybe the charter company filed the flight plan to the wrong city.