This article is written from an out-of-universe perspective for better explanation of game and story mechanics for using these terms.
Spacetime
Spacetime is used to refer to the combined dimensions of space and time where space as we know it consists of three dimensions by which things can be measured (length, width, and height). Time composes a fourth dimension where an object can be measured to have a position and velocity just as in space. Any object in space can move in any or all of the three space dimensions relative to any other object in space. Likewise any object in space has a corresponding relative location and velocity in time.
Reality vs. Role Playing and Storytelling
While in actual physics there is much debate over the construction of space and time or spacetime for the purposes of the role playing we are assuming that the above dimensions of spacetime are mathematical constructs designed to allow people to conceptualize and measure the universe in which they live. As such there is no "Time Dimension" that can be traveled to, nor is there the absurd notion of a length dimension. A four dimensional spacetime is simply a way of describing position and velocity, relative from one object to any other object.
Subspace
Heavily used in Star Trek as well as other series, the term subspace refers to the idea of layers of space where subspace exists adjacent to and intertwined with normal space. Star Trek doesn't really get into the mechanics of this since as a plot element subspace is used as a kind of scientific catch-all that either causes or contains strange and wonderful things for the characters to deal with.
Being Vague
It is suggested vaguely that magnetic and / or gravitational fields are in some way related to subspace and it is possible to create a 'subspace field' that is either used to manipulate underlying subspace or provide a bubble of space within normal space but separated from normal space by the field. Subspace is also suggested to have something to do with the flow of time and it is said that by manipulating subspace fields one can modify how time flows or how a person flows within time. Again, the specifics are left rather vague and sometimes contradictory.
Principles
For the purposes of role playing it is often not necessary to go into the exact theoretical mechanics of subspace, as a plot element it often needs to be barely defined, if defined at all. Should a person which to provide some kind of continuity in using subspace at a plot element (or simply put, to use the term 'right' in a story line or technological explanation) here are the basic ideas at work, to avoid confusion...
Subspace can be conceptualized as the infinite layers of space between planes of reality. In Star Trek it is said that there are subspace domains, like a honeycomb with an infinite number of cells. Each domain is subject to a different (sometimes completely different) set of physical laws and relationships than exist in normal space. This is mixed with the idea that these subspace domains increase in their difference from normal space the farther away they are from normal space - or to be more accurate, the more energy that is required to access any particular subspace domain or layer. Because these layers of infinite a layer of subspace that is directly adjacent to normal space can be very slightly different from normal space in terms of the laws of physics that operate within that layer. For instance, the Warp Field created to propel a starship is a subspace field that creates a bubble of subspace in which the normal physical laws governing the speed of light and general relativity can be bypassed. This is conceptually similar to the generalized propulsion concept of "Universal Parameter Change".
Matter & Energy
Time, Speed of Light, Relationship between Matter and Energy, and virtually any other physical law and relationship can be changed (or rather a subspace domain which contains the desired attributes can be found) given that normal space is manipulated in such a way to allow a ship to pass through or a bubble is created to artificially contain such a region of subspace. To do this requires the creation of specific matter and energy configurations, the more exotic the attributes required the more exotic and more difficult it is to create the desired space.
Because time can flow differently in different layers of subspace it can be used to travel through time, in the Solas Tempus universe the Dimensional Fold Drive uses a subspace bubble to manipulate the flow of time in this way. Wormholes, black holes, and any other exotic phenomena thus has something to do with subspace in some way.
Hyperspace
Hyperspace as used in the Solas Tempus universe is derived from Hyperspace as used in Babylon 5. Thus it is conceptualized as a complete separate and foreign region of space for which every point in Hyperspace has a correspondence point in normal space. As such Hyperspace is defined here as being a very specific domain of subspace. This domain is accessed through jump points that only flow one direction. A jump point can be created by a large gate structure or by ship with the sufficient energy production requirements to create a jump point on their own.
Exiting & Entering
A jump point is required to enter and to exit from hyperspace. Without an exiting jump point a ship could be trapped in hyper space forever.
Beacons are used to navigate in hyperspace because there are definite currents in hyperspace, without a navigational lock on a beacon or another ship (that assumability has a lock on a beacon or can exit hyperspace at will through creating its own jump point) a ship would have no way to navigate within hyperspace to find a gate to create an exiting jump point. This makes it extremely easy to loose a ship in hyperspace with no hope that they will ever return.
Limitations
For the purposes of technological compatibility in Solas Tempus it is a well known fact that Warp Drive cannot operate while in hyperspace. It is enough for most stories just to have this known to be true. In the event more clarification is needed it can be most easily said that creating a warp field within hyperspace folds back in upon the ship that is generating it and thus can extreme damage or even destroy the ship in question. All ships with Warp Drive must vent all drive plasma from the drive coils to avoid this. Safety protocols are in place at any jump gate that will prevent a ship from entering a jump point they create unless they can detect the warp drive is inactive in this way. However, the warp core may remain active providing ships power, as the warp coils are the actual mechanism for creating the dangerous warp field not the warp core itself.
Possible Problems
As a side note, a Romulan ship that uses a quantum singularity as a warp core could be thought of as problematic except that in the storyline of Babylon 5 the Membari White Star's use a gravity drive for propulsion, thus in the Solas Tempus universe this is used as an excuse to afford Romulan Warbrids the same rules as other ships with warp drive.
Because transporters use a subspace domain for transmission of the matter-stream from one system to another this also sould be considered problematic and it has not yet been decided if a transponder system can function within hyperspace.