1. Entropy and information are basically opposites. Entropy tells you how many quantum states are consistent with the information you have. If you have more information about the state, then there are fewer states that match the description, so the entropy is less.
3. When two particles interact, they trade some energy and momentum. The amount of energy/momentum transfer is in superposition. Somehow, the wavefunction collapses, and the amount of transfer takes on some random value. So, if we initially knew the energy/momentum of each particle before the interaction, afterwards we only know the total. So some information was lost. It's not clear how this wavefunction collapse occurs.
I dont know much things about wavefunction actually I am freshman at physics :)But, wavefunction collapse is not a unitary transformation.
I searched a bit and says theres no such conservation but From unitarity or cpt there could be
"CPT seems to imply it. You can reverse the system evolution by applying charge, parity and time conjugation, so the information about the past must be contained in the present state. That implies conservation of information by the evolution.
Sure, that's fine if it doesn't interact with anything.
I ll look when I can.Thanks :)Look here, and Google black hole paradox for more discussions like this, if this anything along the lines of what you are wondering.