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The windows opened because the relays for them are in the alarm module.....
Unfortunately I think you are going to have more than just a burned out alarm module, I'm a few cases I had to fix firsthand when the module was submerged out would activate the locks, over and over, which burned them all out, meaning both door latches, fuel door lock, and the lock which secures the cable releases for the hood and trunk.
My advice it do get everything dried out, then check all the connectors for corrosion, clean accordingly.

Most importantly you need to find out where the leak is....
It is most likely clogged rear drains....
Remove the rear speakers (2 torx20 screws) and there are little drain trays right behind each speaker....probably clogged with leaves....

I had one car where aftermarket stereo guys left a grommet out of place when they ran some wires, water would just pour in......