Bloody hell, I skip out for a few weeks to move house and all hell breaks loose. I'm still in the middle of moving both home and business, so won't be back properly for a while. But let's just clear up a few things:
CTCs are an everyday part of General Relativity. They crop up in many solutions, most famously the Kerr-Newman family of black holes, the Godel space-time, and suitably accelerated wormholes.
The Chronology Protetction Conjecture is precisely that - a conjecture. It is the observation that space-times that admit CTCs are typically unstable to perturbations (which you can understand from the idea of particles trapped on inifnite circuits of the CTC creating a diverging stress-energy)
The field equations of GR are certainly local, but that does not prevent global topological non-triviality, including black holes, CTCs, wormholes, etc.
Microscopic-scale CTCs are certainly possible within the context of the "quantum foam", should it exist. CTCs are a feature of space-time physics, not just the Einstein Field Equations (GR)
Photons do not have mass - but they do have momentum.
Lots of tripping up over various uses of the word "time". Acceleration does not make "time" "speed-up". Acceleration simply means you are changing your path through space-time. The more you accelerate, the shorter your path between two fixed events, relative to someone who travels between the two events without accelerating. The length of the space-time path is the time experienced along that path.
The dimensions of time and space are warped and curved by the presence of stress-energy (mass, momentum, charge, etc), and this too will affect the length of paths taken through space-time. Which is why the mass of the Earth affects the rate at which clocks tick.
Lorentz transformations are part of Special Relativity, not General Relativity, and have little to do with the maths/physics of CTCs (LTs are still approximately relavant in sufficiently small volumes of curved space-time)
Right, work to do...
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