So when people say: 'I am approaching the speed of light, and to get to 100% light I would need infinite energy' they are essentially saying that this situation is impossible?
Yes.
I read this in Hawking's book and confused me because I assume when he says 99.9% speed of light, he means 99.9% speed of light in relation to someone outside observing?
Yes, but note that $c$ is a universal constant. If something is traveling at the speed of light, it is traveling at the speed of light to everyone (except other photons traveling parallel, see my answer to this question).
I just cannot understand this notion of needing more and more energy to get closer to light as absolute velocity does not exist? (in that it is a purely relative concept).
It boils to relativity. The energy of a particle is related to the velocity, $v$, via the relation
$$
E=\gamma mc^2=\frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}
$$
As $v\to c$, $E\to\infty$, but gives an indeterminate operation at $v=c$.
Surely the ability to accelerate further cannot possible be impeded because speed is all relative, there should be no limit to acceleration? If I 'accelerate' a further 50MPH, will I get to the destination exactly 50 miles early?
(a) 50 mph is a speed, not an acceleration and (b) you can't get somewhere "50 miles early." If your trip is 300 miles, you can't get there in 250 miles. You can get there in a shorter amount of time.
From what I can gather you 'can' accelerate FTL (sort off) but instead space bends towards you so you will get to your destination 'ftl' but only due to the curvature in space? So in effect, you can go light years in seconds (lets forget the practicals for a second), but from anyone observing, this will ALWAYS take light years.
The 2nd postulate of special relativity states that $c$ is invariant of reference frame (constant for everyone), so nothing can accelerate to speeds faster than light.
Also, if for me I am going 'FTL', does outside observers see me as going light speed, or is it 99.999%.. is there a specific number?
Faster than light means that you have a speed $v>c=2.9979\times10^{10}$ cm/s. If you have done this, then kinematics suggest you have a complex velocity (as in the imaginary number complex) which is utter nonsense since velocity is a physical (real) quantity.
Imagine that there is a person who prefers to measure the amount of money in his bank account with the value $V$. The equation is $V = C\tanh N$, where $N$ is the actual amount of money in dollars. This person will also be confused:
Why is there a limit ($C$) on the amount of money that I can have? Is there any law that says the value of my money, $V$, cannot be more than $C$?
The answer is that he is just using a "wrong" variable to measure his assets. $V$ is not additive — it is a transform of an additive variable, $N$, which he has to use in order for everything to make sense. And there is no "law of the universe" that limits the value of $V$ — such a limit is just a product of his own stubbornness.
The same thing applies to measure speed — it is the "wrong" variable to describe the rate of motion; speed is not additive. The "correct" variable is called "rapidity" — it is additive, and there is no limit on it.
Best Answer
Backing up what zeldredge said, what you asked about is known as "relativity without light". According to the intro of this paper (arXiv link) for instance, the original argument was given as early as 1910 by Ignatowski, and has been rediscovered several times. There is a modern version due to David Mermin, in "Relativity without light", Am. J. Phys. 52, 119-124 (1984), but a pretty accessible presentation may also be found in Sec.2 of this paper by Shan Gao: "Relativity without light: A further suggestion" (academia.edu link). The basic idea is that the existence of an invariant speed follows directly from the homogeneity and isotropy of space and time, and the principle of relativity. No reference to a speed limit is needed, but it does follow that the invariant speed acts as a speed limit. The only alternative is a universe without a speed limit (infinite invariant speed), where kinematics is governed by the Galilei transformations. Why it is that our universe has a finite invariant speed, and not an infinite one, remains an open question. Gao's "further suggestion" is that the invariant speed is related to the discreteness of space and time at the Plank scale, which is an intriguing thought in its simplicity, but then it remains just a "thought" so far.