Sails don’t billow into the wind. They are set at an angle to it. Just enough to inflate them, creating an airfoil. The remaining wind blows across the airfoil, creating “lift” (like vertical airplane wings) that pulls the boat along more efficiently. That’s why sail boats can actually go faster than the wind.
From this photo, the wind is blowing almost parallel with the sails.
The type of sail you’re referring to is ‘bermuda-rigged’, like the smaller ones at the front of the boat in the picture. The big ones in the middle of the picture are ‘square-rigged’ which are really only good for sailing downwind.
I think the square rigged sails could be rotated, so you could sail with a cross wind. You would just have a fair amount of trouble sailing upwind.
Maybe, although I haven’t seen anyone doing it. I’m guessing you would need a sheet to each corner to trim the sail tightly enough which I think would be too much of a headache for the crew. Worth thinking about tho, especially in a castaway situation!