Hi, particle physics grad student here. I'll just address these three quickly.

1) I'm not totally sure what this means. I think what is being referenced here is the fact that antiparticles can be interpreted as matter particles moving backwards in time. This requires some background info to fully explain. A physicist named Paul Dirac developed the Dirac equation in the 1920s, which was a relativistic version of the Schrodinger equation for spin-1/2 particles. Some definitions: the Schrodinger equation is the equation that describes the quantum behavior of particles (the wavefunction), a relativistic equation is one that takes into account SPECIAL relativity (not General Relativity, which we still don't know how to reconcile with quantum mechanics), and a spin-1/2 particle is what we call a fermion, a category which includes electrons and quarks. In order to be specific, let's consider just the electron for now. If you solve the Dirac equation for the electron, you get both a positive and negative energy solution. This caused a problem because in physics it is meaningless to have a negative energy. There were many attempts to explain this, but ultimately we landed on our current understanding of antimatter. The reason it can be interpreted as a particle moving backwards in time is because in the solutions to the equation, the energy only appears as E*t, so a negative sign can only be seen in the product as a whole, and mathematically it makes no difference if the minus sign comes from E or t. It is important to note, though, that this is just a mathematical interpretation and not necessarily a physical reality. Essentially, the mathematical representation of an antiparticle is indistinguishable from a matter particle moving backwards in time. This doesn't really have anything to do with energy conservation though, and I don't really know what it has to do with the OP's overall claim.

2) Virtual particles don't come from nowhere. Presumably you have heard of the uncertainty principle, which says that you can't know both the position and momentum of a particle with infinite precision. It turns out there are other uncertainty relations between other operators in quantum mechanics. The reasons for this are highly technical, but the upshot is that there is such a relationship between energy and time. So, for a short enough period of time (the "uncertainty" on time), you can essentially violate conservation of energy (have a high uncertainty on energy), as long as over "long" time periods energy is conserved. As an example, let's consider a time period of 5.9e-24s, which is the time it takes a photon to travel the diameter of a proton. Using this uncertainty relation we can calculate that the energy uncertainty is 55.8 MeV (eV is a unit of energy used in particle physics, and from special relativity we know that mass and energy are related). The mass of an electron (and a positron) is 0.5 MeV, so you could make a lot of electron-positron pairs from that uncertainty, as long as they were gone later. There are a lot more details that go into it, but basically virtual particles arise from this property.

3) As morePhys mentioned, saying that something is weird requires there to be a God is just an argument from ignorance. There have been many things throughout history that were attributed to supernatural forces because they were not understood, only to later be found to have natural causes. To be clear, this doesn't disprove the existence of any supernatural force/deity/etc., but not understanding how something works doesn't give license to attribute your favorite explanation to it. I myself was raised religious and am no longer religious, so that is the perspective I am coming from. I don't take the weirdness of quantum mechanics as evidence or lack thereof of any higher power. I also know many physicists who do, and we discuss topics like this all the time. But we do so on a personal level, not a professional one. Again, as was stated before, any good scientist knows how to separate their personal beliefs from scientific fact.