1. Water freezing as ice adds weight and unbalances the control surfaces, making them more prone to flutter. The US Navy had similar problems when they put too many layers of paint on top of the other thus adding weight and unbalancing some control surfaces.
2. That would not be too hard. First of all how do we know it was not freezing at the surface? How fast were the investigators there? The recording of ice and/or other perishable evidence are among the initial actions investigators do when arriving at an accident site. Either way, evidence of control flutter is very easy to spot, and there are not many ways the control can get unbalanced. If you add on top of that the fact that maybe some drain holes were found clogged, that it was rainy at the departure airport and control unbalance due to icing is a known problem, it wasn't too hard to figure out the cause of the flutter.
Evidence of control flutter is common at many accident sites. However that is mostly due to overspeed. In this case they might have calculated that the speed at which the flutter occurred was not beyond the aircraft's envelope.
If you read the accident reports for the flight in question I'm sure you will find more explanations.
palgia