Point 1 is wrong. Time dilation is not due to a change in difference between emitter and receiver. Such a difference change produces a Doppler shift, which is a separate effect. Time dilation is where two reference frames measure different time intervals between two events. So, for example, if you had two emitter/receiver setups. Each with a constant and equal distance between each respective pair, and these two setups were in motion, Then an observer at rest with respect to either of the setups would note that the time intervals between transmission and reception would differ between the setups.
Point 2 is also incorrect. In such a mechanism, the purpose of the wound spring to to counter losses due to friction. It doesn't take any force to keep something moving at a fixed angular speed. If you were to remove friction from the example, the hand, once moving, would just continue to rotate on its own without any further input of force. This would not change due to the overall motion of the mechanism. The clock hand would be measured as moving slower by someone that the mechanism is moving with respect to, but this is due to their measuring time intervals differently, and not due to some mechanical effect acting on the mechanism.
Point 3 is, again, incorrect. c is the "speed limit" in the universe because it is an invariant speed. If something ( like light) is moving at c, then everyone measures the light as moving at c with respect to themselves, regardless of the relative velocity differences between those doing the measuring the light. A universal speed limit equal to this invariant speed automatically follows due to its mere existence.