Update: There is now a wiki entry for voidlife, which supercedes this.
The most likely hazard of deepspace fauna is the voidshark. A smaller relative of the voidwhale, it is a pack-hunting predator. While voidwhales and kraken are their usual prey, they will eagerly take "bites" out of jump fields. If the field generator can't sustain the field, the ship will drop out of jumpspace early, never to be seen again.
Some spacers believe the voidshark is not really gaining sustenance from the jump field - they don't draw nearly the amount a void leech of a similar size can, they just do it in a more abrupt fashion. Instead they suspect the voidshark is either trying to drive the "competitor" out of its territory or, possibly, just trying to figure out what it is.
Voidwhales
Update: There is now a wiki entry for voidlife, which supercedes this.
Voidwhales live almost entirely in deep jumpspace, the aphotic zone, dipping into a bright zone only periodically on feeding runs that can sustain them for years.
Adult whales can easily keep up with or even outpace starships, though most of the time they move at a leisurely pace, taking a month or more between brightspaces.
Their intelligence is a matter of debate. Zhdez believe they are intelligent but that their alienness makes it difficult to measure -- they can be telepathically contacted but full communication has not been achieved. They seem interested in starships, and a pod will sometimes "swim" alongside one for some time.
Harvesting voidwhales for brightspace energy is possible. It's necessary to kill an entire pod to prevent retribution - even if the whaler dives back into realspace after a kill, the rest of the pod will camp the bright point until it returns. Harvesting the entire pod requires a fleet of ships, so either the energy from the others is wasted or a large number of ships - likely to alert the whales to danger - is needed. Voidwhale harvesting is prohibited across charted space, but since the equipment is the same as harvesting kraken and the energy is the only thing returned, it is assumed to happen sometimes when the opportunity arises.
Voidleeches
Update: There is now a wiki entry for voidlife, which supercedes this.
Voidleeches live in the fringes of brightspace and are nuisances who hitch onto a starship's jump field and feed off its brightspace energy. Unless there is a significant swarm and a ship is critically low on energy, their chief threat is economic - though liners particularly hate them since they tend to frighten the passengers.
The larger they are, the slower they are, so small, nimble ships can easily avoid them. Larger ships may often not find it worth the energy expenditure to avoid small ones.
They can be killed by an overload, so cycling energy into the jump field will clean them off. If they become too numerous in an area, local starports may offer extra fuel to outbound ships who agree to encourage swarms to latch on and be pulsed, or offer bounties to brightfishers.
Algae, seaweed, krill, and bunker
Update: There is now a wiki entry for voidlife, which supercedes this.
Most of what lives in the bright zone is the jumpspace equivalent of plant life up through small schoolfish. Lower in energy than the larger voidbeasts, but there's much, much more of it. Sweeping it up (with an extended jump field?) is slow but reliable, and fairly safe. Sure, the occasional space pirate might demand you refuel them, but they're not going to hurt you or damage your ship as long as you don't refuse them.
A comber ship is going to jump into brightspace and spend a week out mostly in the fringes of the false star, just trawling through with a big low-grade jumpfield extended, collecting biomass and then collapsing the jumpfield into energy containment (waves hands vaguely) as it drops back into realspace and the jumpspace-native creatures dissolve into ~~mana~~ energy.
There are probably "fishing" permits, since a busy starport's needs could otherwise justify enough combers to wipe out the biosphere of its brightspace point.
Brightspace navigation
Update: There is now a wiki entry for jumpdrives, which supercedes this.
So if I assume a single level of jumpspace, then maybe navigation is a matter of the known contours of the local false star. You pop out in the exact center, and you know either from navigation charts or just what you saw on the way in, which way you've ended up oriented relative to jumpspace. And you just know that, for example, if you align yourself this way with the major space-kelp beds, you'll come out of the bright zone with Sundtia's false star in sight.
If you come out on the wrong side of the false star, it may take some hours to backtrack (either around, or back through if the star doesn't have a lot of navigational hazards). Probably not enough to be a problem with the jump field timing (I want the ships to spend most of their time in deep [jump]space) but enough to be a problem if your passengers are trying to connect with a scheduled vessel.
Do you have to drop out of jumpspace in the exact center of the false star? Probably not, but the closer the better. But that's also where the pirates are likely to be lingering.
Jump level spitballing
Update: There is now a wiki entry for jumpdrives, which supercedes this.
Now I'm trying to decide if I want quantum levels of jump after all.
Maybe you come out in brightspace and that's it. You have to navigate out of the brightness (photic zone?) of the local false star before you can see the other stars, and then you have to just navigate across the apparent distance between them.
What if: Jump fields last a week, regardless, and drive rating is how fast you can get your jump field to push you. So a J2 ship will get to a star a hex away in three and a half days, but it can't just decide to stop there and pop out of j-space to arrive much faster than a J1 ship.
Complications: It does mean they can pass off messages to ships with older jump fields, so faster-than-starship communications are possible. You probably can't merge jump fields that are too far off in charge level (so no dropping off passengers onto a lower-charge ship).
Ooh, but that leads to some wild possibilities: I don't want the charges to have to be identical (that eliminates brightspace piracy), but they should be similar-ish: so it would work to have a day-4 vessel come in, let its passengers off on a day-5 vessel, which then lets them off on a day-6 vessel, then a day-7, and then they can drop out of brightspace. Such a cascade would probably be expensive and/or risky, since merging jump fields is a touchy process. Perhaps you can merge fields two days apart but the risk is so much higher that doing so violates Naval standards outside of an emergency, etc. etc.
Of course, a J2 ship on a day-4 field could just be diverting, and have to sit in a holding pattern until the jump field ages enough to drop into realspace. It doesn't get you to the planet any faster if that's your emergency, but if you don't have enough left in your week to actually get to the farther planet (say you're on day five instead) it's the best you can do.
Brightspace
Update: There is now a wiki entry for jumpdrives, which supercedes this.
Nope, nope, I was wrong, there are definitely jump-0 drives, because brightspace is where the fish are. And I have found my unobtainium: brightspace energy.
Brightspace energy is hard to harvest directly, because you tend to spend more on maintaining your jump field than you do collecting with solar panel analogs. But the fauna and flora of jumpspace don't need jump fields, so they collect it naturally. There is the brightspace equivalent of algae and seaweed and whatnot, and then the equivalent of fish, all the way up to the equivalent of whales and giant squid and whatnot, the latter of whom can leave brightspace and migrate from star to star.
It's probably euphemistically called "mining," but j-0 vessels can climb into brightspace to harvest the flora or net the fauna. Dropping back into realspace with brightspace matter converts it into energy, which the mining vessel stores in batteries (probably a containment field of realspace energy rather than some unobtainium).
The equivalent of Traveller fuel scoops and refining equipment is the energy-capture equipment. Can one jury-rig it for a ship that is arriving in a gate (stepping down to local j-0 in the process) without enough fuel to return to jumpspace? Maybe?