Is space-time a special form of energy? I know space-time can be influenced by matter and energy, so it must be somehow mingled in with the mix of it all, but does space-time have a fundamental particle? Can we make a little bit of space-time with enough energy? Might the Planck length & time quantize space-time?
 A: Spacetime is not a physical object, it is a mathematical object called a manifold. More precisely it's a differentiable manifold equipped with a pseudo-Riemannian metric.
I realise the Wikipedia articles I've linked aren't going to be much help for the beginner, but I'm not sure how else to define spacetime without being misleading. In essence the manifold gives things directions to move in, and the metric measures how far those things move. The point is that you can't make spacetime because it isn't a physical object that takes energy to make.
Your question about quantising spacetime is a separate issue and is dealt with in lots of other questions on this site for example Is spacetime discrete or continuous?
A: It seems relevant for OP's question to mention the notion of energy in GR. For a generic spacetime manifold $(M,g)$, one cannot associate an energy $E$ (or equivalently, a mass $m=E/c^2$), cf. this Phys.SE post and links therein.
However for restricted classes of spacetime manifolds $(M,g)$, it is possible to associate a mass, such as e.g. the ADM mass. Typically such manifolds have a global temporal Killing symmetry, and asymptotically approach a reference spacetime $(M_0,g_0)$. The reference spacetime $(M_0,g_0)$ could e.g. be Minkowski spacetime.
Examples: 1) The ADM mass $m$ of Minkowski spacetime is zero, because it is equal to the reference spacetime. 2) The ADM mass $m$ of the Schwarzschild metric is $m=\frac{Rc^2}{2G}$, where $R$ is the Schwarzschild radius.  
A: The Einstein field equations relate matter to the deformation of spacetime, i.e.
$$\underbrace{R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R}_{\text{geometry}} = \underbrace{8\pi G T_{\mu\nu}}_{\text{matter}}$$
However, $T_{\mu\nu}=0$ does not imply a trivial solution. A non-trivial solution such as the Schwarzschild metric which describes a spherical body, e.g. a black hole is a solution for a totally vanishing stress-energy tensor. However, as indicated in another answer, we may associate a mass to the solution,
$$M=\frac{R}{2G}$$
in natural untis where $R$ is the Schwarzschild radius (distance from the center to the event horizon) and $G$ is the four-dimensional gravitational constant. As expected, in the limit $M\to 0$ $g_{\mu\nu}$ reduces to,
$$\mathrm{d}s^2 = \mathrm{d}t^2 - \mathrm{d}x^2 -\mathrm{d}y^2 - \mathrm{d}z^2$$
which is flat ($R^{a}_{bcd}=0$) Minkowski spacetime, as expected.


Does spacetime have a fundamental particle?

Spacetime itself is a manifold, and we do not associate a particle which literally comprises spacetime. However, the graviton is a gauge boson of spin $2$ which is believed to act as the mediator of gravitation which is represented or interpreted as the deformation of spacetime.
