I am going to try and answer these from a completely sceintific perspective, because I don't think they have been very well answered yet, no offence.
1. Science has conservation laws that prevent some things being created or destroyed. Mainly these are a consequency of symmetries in the laws of physics. For example, energy can't be created or destroyed, which is a consequnce of time translation symmetry of the laws of physics (the laws today are the same as yesterday). Particle number is not necessary conserved, though fermion number is. So electrons, for example can't be created unless a positron is also created, and they must "use" energy that is already there - they can't just create it. Photons however can just be created as long as there is enough energy.
So the problem with the Big Bang creation is not really where does the stuff come from, but where does the energy come from. And indeed, was there a space-time background on which to build it? While we actually have no idea how the moment of the Big Bang happened (there is no data on this whatsoever) there is no reason to believe that it is not possible theoretically. Even if the moment of the Big Bang were the first moment in time, then one cannot apply a symmetry argument to time translations beyond this boundary and therefore (logically) can't insist on energy conservation.
One cannot say "why" the Big Bang happened, but sceince does not attempt to ask why - it only asks how.
2. I don't think it is any easier of harder to be honest. (But see 3.)
3. God (that is, some being with power to change the laws of physics) is by definition transparent to science. Science relys on observations and only declares an obervation as valid if it is reproducible. If you do an experiment twice and get different answers, you need to figure out why by making more observations. And if you get a particular result only once and cannot reproduce it, you throw it away assuming it is faulty. Any act of God would be an irrepreducible event and not be interpretable with science. Science wouldn't even consider it. (This is in much the same way that an individual's actions are themselves not valid scientific events - it is only why you analyse behaviours of groups that you can then say something about individuals in a statistical sense.)
4. Presumably He doesn't have to abide by the laws of physics. To my mind, this is pretty central to the definition of God in the first place.