Not inside the Alamo. I was told by security after I took one picture. Not even without a flash.
Yes you can, and yes you can take pictures inside. There are restrictions at The Alamo (run by a private firm on behalf of the state), and commercial restrictions in the diocesan buildings at the missions, but generally you wont have trouble with photos.
Yes.
Absolutely
Yes, any place you are allowed to tour
Yes anywhere you like. I took pictures in all buildings.
You can take picrures outside but not inside of the museum
Sure you can
Yes you can.
Yes. Just not inside.
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