Hyperspace goes by several names. Hyperspace, of course, and also bluespace, greyspace, and redspace. It is commonly believed that the source of the alternate names is the strange doppler effect that takes place within it for unknown reasons. This is an 'alternate space' to "realspace", but seems to be different than realspace in how it reacts to everything, and is so closely attached that it is actually effected by objects in realspace. Within hyperspace, there is no c limit, and everything behaves as if it were massless. Inertia has no place within it either, and this proves to be the property that makes it worthwhile to visit in the end for most races. There is also a strange ambient grey light throughout it. In the event of an object switching between realspace and hyperspace violently, it can inflict major damage to anything surrounding the object where it switches for a few moments afterwards in what is best described as a "rip"
Hyperspace is full of distortions, all of which are centered around objects of mass in realspace, which are capable of damaging anything that enters them while in hyperspace. There is also the quirk that a fast enough object traveling in hyperspace naturally will start taking minor damage. As noted, there is no c limit within hyperspace, but the limiting factor for this is the stabilizers of a hyperdrive, which keep a vessel from actually encountering damage from the distortions of hyperspace. They can be overidden, but this is highly unadvised. The drive itself serves to shift a vessel over, give it a large initial boost in the desired direction, and keep it within hyperspace at a large energy cost. The stabilizers do, however, definitely help to lower the energy cost to remain within hyperspace by a significant amount. The drive takes little mind of a starship's mass, so a corvette and a titan have less than a MW of power difference to transfer to hyperspace, and it also does not require very much increment to size in order to handle a larger ship.
When using hyperdrive for transit, the stabilizers use large amounts of power to keep a ship within hyperspace safe from damage by distortions or speed, along with making it possible to maneuver to greater degrees or leave hyperspace at any point desired. They will automatically force a vessel's hyperdrive to shutdown if they are overwhelmed by a distortion the craft encounters, but if a sufficiently large distortion is hit suddenly, vessel damage and/or destruction may occur before the stabilizer can cut the drive. They also limit the speed capable of being traveled in order to keep the odd stress induced by normal travel from surpassing their ability to nullify and damage the vessel. This speed limit starts off rather low, and takes a lot of time and effort to increase by even small margins.
Without stabilizers installed, one can theoretically travel significantly faster due to the lack of safety inhibitions, but it requires a precise calculation of where a vessel is to drop out of FTL prior to jump, a significant amount of structural reinforcement and armoring to survive the speed induced damage, supplies to repair the hull as needed, and a large cooldown period in order for the drive to recharge and cool down from what is best described as overheating. The only effect a ship without stabilizers is capable of inducing on its course after entry into hyperspace is on its speed, usually accelerating as far as their reinforced structure can handle. Another key note is that when a ship does not have a stabilizer installed, it may induce a rip in realspace and hyperspace. This rip is temporary, lasting only moments, but is extremely dangerous to anything that makes contact with it.
There are theories of 'hyperwarp' thrown around by some academics, however this idea is normally looked down upon with disdain by the majority of the science community. This is due to the simple fact that hyperspace does not like being warped or distorted from within. Attempting to use a warp drive within hyperspace is likely to end catastrophically, as it instantly creates a massive traveling hyperspace distortion centered around the attempting craft, capable of ripping even the most reinforced vessels apart if they are not equipped with stabilizers to escape hyperspace. This is believed to be related to the different universal laws in play governing it.
When a vessel uses Hyperspace for transit, it cannot make sharp turns while moving without risking significant structural damage. To turn within hyperspace is generally inefficient as a result of this, often requiring a full stop of the vessel or a massive bend. The former is a curse to smaller nations, the latter proves to be somewhat an inconvenience for larger ones. In the case of most craft, bar only the most heavily reinforced and armored craft, it is very much preferable to drop out of FTL, and fire an RCS burn to rotate the craft. Entrance into hyperspace cancels out most if not all angular velocity, so this method has little risk to it in the case of a powerful RCS system.