Q1. As the charging port is only supplying DC for charging something it shouldn't have anything to do with the data lines in the other ports so I don't see why your idea shouldn't work. Just make sure the Pi doesn't draw too much current.
Q2. 12v rechargeable batteries generally supply just over 13v when fully charged, which will drop slightly to 12v as they are used. Your hub should be designed to have a bit of leeway with the supply voltage (for safety) so I don't see why it shouldn't run ok from your battery.
Q3. It's not designed for outdoor use so yes, a suitable housing would be a necessity.
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