Hope I understood your question.
About the speed of light, since you can' t see any object travel faster than light, you cannot be observed as faster than light as well. Thus you can' t reach speeds higher than $c$.
About your second question, it is somehow true that Lorentz transformation do not apply to references as fast as light is. We can see what light sees by applying some limit process. It is true that, according to our interpretation of special relativity, light does not see the passing of time, and sees the usiverse as flat. This means, accordingly to what you say, that light reaches every place istantly, with no passing of time. Of course this is just interpretation, we do not really know what' s going on, but the mathematical structure is rather clear, and this is what it tells us.
About your last point, be careful. Taking your time, or the time of someone outside of your "ship" are two different things. Theory of special relativity deals with measurement in one reference frame. If you use your self time, then you have to use your self distance as well. Unfortunately, in your example, you use an accelerating reference frame. Special relativity does not deal with acceleration, only with "inertial" reference frames. For better understanding this point you should refer to some textbook or paper.