1: Yes. Newtonian can be applied since newton introduced consistency, coherence and generality against alternative approaches where phenomena were studied and explained in relative isolation from each other
2: No I won't outline it .....because you want me to.
Again I would suggest it's better not to conflate the concepts of personal coherence to a philosophical concept. I think it's better to use the concept of rationally discoverable laws here, and while i'l happily agree that Newtonian thought (which existed pre Newton, of course) is hugely influential in spheres where both coherence and rationality are assumed, it has it's issues as you stray into to the social sciences and with post Newtonian physics.
At base though the problems as a philosophy appears to me to be the need for the assumption that it describes a reality rather appearance of reality which is, I suppose, just another expression of hard solipsism, and its basis on that idea of reality means that it can only be descriptive.
This then leads to the overall problem for gods of deism and more particularly theism being posited, since if they are part of this they are either bound by it, or they cannot exist. Following this there can be no miracles and the resurrection if it happened is no more important than a fart.