The wide water carries weather further. Damage here is more often wind-driven than debris-driven.
The instinct after a storm is to clear up. Doing so removes the record of what happened, and that record is what an insurer works from. Photograph everything in place first, from more than one angle, including the things that look minor.
On a covered slip the visible damage is usually to the roof, but the more important question is what the roof did to the structure while it was being damaged. A large covered area under strong wind puts significant force into the posts and frame beneath it, and that damage is not always visible from the shore.
Whether a dock can be repaired and whether it is safe to walk on today are different questions with different answers. The second one is the one that matters this week, and it is worth asking explicitly.
Yes, in the first documentation. Wind damage frequently presents as something minor at the roof and something structural underneath, and a claim is far harder to reopen than it is to file completely.