Work is transfer of energy from one system to another OR transformation of energy from one form to another. Either way, work does not create energy.
When I lift an object, I am transferring energy from my body/muscles to the object-earth system. The energy goes into potential energy of the object-earth system because the separation between the object and the earth increases.
When I drop an object, the energy stays in the object-earth system, but is transformed from potential energy to kinetic energy. The gravitational force does the work, i.e. produces the transformation of energy from one form to the other.
Well, the way to find the units of the constant are to consider the equation it takes part in:
$$
F = G\frac{m_1 m_2}{r^2}
$$
$F$ is a force: so it's measured in newtons ($\operatorname{N}$). A newton is the force required to give a kilogram an acceleration of a metre per second per second: so, in SI units, its units are $\operatorname{kg}\operatorname{m}/\operatorname{s}^2$. $m_1$ and $m_2$ are masses: in SI units they are measured in kilograms, $\operatorname{kg}$, and $r$ is a length: it is measured in metres, $\operatorname{m}$.
So, again in SI units we can rewrite the above as something like
$$\phi \operatorname{N} = \phi \operatorname{kg} \operatorname{m}/\operatorname{s}^2 = G \frac{\mu_1 \mu_2}{\rho^2}\frac{\operatorname{kg}^2}{\operatorname{m}^2}
$$
where $\phi$, $\mu_1$, $\mu_2$ and $\rho$ are pure numbers (they're the numerical values of the various quantities in SI units). So we need to get the dimensions of this to make sense, and just doing this it's immediately apparent that
$$G = \gamma \frac{\operatorname{m}^3}{\operatorname{kg} \operatorname{s}^2}
$$
where $\gamma$ is a pure number, and is the numerical value of $G$ in SI units.
Alternatively if we put newtons back on the LHS we get
$$G = \gamma \frac{\operatorname{N} \operatorname{m}^2}{\operatorname{kg^2}}
$$
Best Answer
The distance moved is unambiguous. When we say "John ran 100 meters in 15 seconds", we don't need to worry about what John's mass is. (The more common language here is "body weight", but this is a physics forum). We also don't need to worry what his starting velocity was. Of course, if John started from a running speed, we would expect him to finish the 100m run faster, but that's all. In the same way, statements such as "the distance between Chicago and Toronto is 702 kilometers" are unambiguous.
If you push a box with a $1N$ force in a straight line for $1m$, then you've done one joule of work. It's irrelevant how massive the box is or how fast it was originally moving. Both of these things affect the box's original kinetic energy, but not the amount of kinetic energy you impart to the box.