The two propositions are entirely correct. However your assumption that the cycle is lossy is wrong; there is nowhere for any lost field energy to go, so the cycle perpetuates according to the law of energy conservation. This was perhaps one of James Clerk Maxwell's fundamental insights.
The "kink" in the field is not governed by c, rather the reverse. The kink is the wave energy. Tts speed of propagation c is governed by the electrical permittivity and magnetic permeability of free space, which just happens to work out at the familiar value. It is this which in turn sets the fundamental limit on the propagation of information.
You may wonder then, what is this field that kinks to form a wave? It arises in quantum field theory as a "zero-point" field which pervades all of space and time. At this point, it can be wise to ascribe such things to quantum weirdness and save them for later. Maxwell's classical theory has no such complication and works in all practical circumstances.