If I were you, I would be calling my insurance agent to find out if I was covered for this calamity or not. If you are, then you should turn the problem over to a general contractor and let him figure out the extent of the damage and make recommendations as to what needs to be done to correct all the issues. From that point, it's in the hands of the adjuster and the contractor.

Thank you. That's what I'll do.

Whether they cover it and handle it, or you have to do it yourself, make sure they/you (a) stop the sources of the water, and (b) throughly dry things out before covering them back up. If water got under the flooring, the subfloor will have gotten wet, too, and may have spread water further than you think.

The leaky faucet may just be a coincidence, and not the source.

Two thoughts. First, you could conceivably have a slow leak in the piping from somewhere in the wall due to any number of reasons. Also, if this is an outside wall and you have had really cold weather lately, you should consider the possibility that it could have damaged the pipes (e.g., a hairline crack). I suggest you go out and look at your water meter and see if there is any movement when no water is turned on in the house. Usually a meter will have a tiny indicator in the center that will rotate if there is the slightest amount of water flow (like a leak or drip).

Second, is there any possibility that you have leakage from accumulated snow/ice, or any kind of water ponding? Two weeks ago my nextdoor neighbor had water get into the wall and come out under his kitchen cabinets. The roof over his kitchen is flat, and the outflow drain had gotten plugged with leaves: the backed-up water had gotten under the roofing and come down inside the wall.