This sort of thing— not knowing what Lorentz transformations or inertial frames are— is why people, including me, have been telling you that you don’t know what you’re talking about. This is very, very basic stuff and crucial to understanding the subject.
If you have two separate frames F and F’, then you have two corresponding coordinate systems. How do you map coordinates from one to the other? In the non-relativistic case, it’s easy: you just have a spatial translation (depending on time, if the (constant) relative velocity is nonzero), and the time is the same in both frames. In the relativistic case, it is not; the map between the two is given by a Lorentz transformation, which is a particular linear map.
An ‘inertial’ frame is a non-accelerating one. Again, this is exceedingly basic stuff. You should know this already if you’re trying to disprove relativity. This is the sort of thing that makes me and other conclude that you don’t know what you’re talking about.
You are confusing two questions: Why is the speed of light constant in every (inertial) frame, and how does SR enforce that? The first is because it’s confirmed by experiment. We could have a completely non-relativistic, Newtonian universe; we just don’t. For the second, there are two possible approaches. One is to note that SR takes the speed of light invariance as an axiom, and then works out coordinate systems have to transform in order for that to work. The other is to just take those coordinate transformations as given and show that they make the speed of light invariant.
Your assumption is incorrect. A Lorentz boost is the coordinate transformation corresponding to a frame moving at a constant velocity; it includes both a length contraction (in that direction of motion) and time dilation. (In general, a Lorentz transformation may also include a spatial rotation, but nothing interesting happens there.) This is, again, stuff covered in the first problem set of a introductory class on SR.
If you want to make precise statements about the world, you have to use math. If you had just asked something simple, like what happens in relativity if you’re travelling at a speed v > 0 and then emit a photon, then we could have answered that easily and concisely. If you want to make the argument that math fails to describe the real world, then you’re a century too late: we already have electricity, GPS, particle accelerators, and all sorts of brilliant technology that happily work with math.