Shannon entropy is just a generalization of thermodynamic entropy. Yes
Yes information is physical.
if you have all the information about a system you can use it to extract energy from it and do work by manipulating the particles of the system out of thermal equilibrium. But increasing information requires some kind of computation which increases entropy because it requires energy, so second law cant be avoided.
If you have a system in thermal equilibrium and you separate two parts of it with a door, and you have all the information about the system you can open the door each time a fast particle comes to it and let it in one part and when a slow one comes let it the other part. So you will make one part hoter and if you get rid of the door you can extract energy from the heat flow. But to get that information you need a lot of computation and for that a lot if energy