Major nitpick: you've got a habitat that's 6000km across, presumably with a conventionally earth-density-and-pressure-and mix atmosphere in it. From the centre ofthe habitat, you're looking through 3000km of air. On earth at standard temperature and pressure, a square metre of surface has about 10.3 tonnes of air pressing down on it. A cuboid of air 3000km long has more like 3675 tonnes of air in it. Even totally clean air without a trace of haze, dust or cloud is not perfectly transparent... various optical effects conspire to reduce its transparency. On Earth, looking straight up, the air mass above you will consume about 14% of the intensity of incoming light, or .16 magnitudes. Lazily using the same equation (proper calculation of absorption and scattering seems like too much hard work right now) it suggests that the centre of your habitat will see a 57 magnitude attenuation in sunlight intensity. Our sun as seen from Earth has an apparent magnitude of -26.74. Its effective magnitude in the middle of the habitat will therefore be 30, which is so faint that you need something like the Hubble Space Telescope to see it.
Most of your worlds therefore will be clustered around the walls of the habitat, and the further they drift from it the darker and redder the light will get until you descend into the black depths.
There will be some weird effects to do with air density being higher around the worlds, of course, and more problematic issues with worlds being gravitationally attracted to each other which will make them all glom together over a long enough timescale. I won't worry about those things here, but you might do well to consider them.
I suggest you have a read of Engineering Virga, a discussion of the nature of a hollow air-filled habitat that is more like 8000km across. It too is filled with small habitats, but they spin to provide their own gravity (and so the issue of mutual gravitational attraction is avoided), and there are artificial light and heat sources that habitats are clustered around (and so the issue of light extinction is avoided). The article is interesting even if you don't bother reading the stories associated with it.
But now lets turn to your actual questions.
How can they get off of their planets?
You might be able to fling some stuff into the void mechanically... the escape velocity of these worlds is only 62.6m/s, which is faster than a sling will fire a bullet but a lot slower than a decent crossbow (which could manage >90m/s even with medieval technology). I'm not going to do any drag calculations to see if the bolt would in fact escape, but the possibility does exist. Note that this means that projectile weapons should be used with extreme caution as you could throw or fire projectiles right around the world and shoot yourself in the back. Projectile weapon tactics are likely to be interesting on these worlds. Incidentally, I wouldn't want to launch a ship this way as accelerations will likely be neck-breaking.
The most sensible way though would be with a ladder (or a tower). If you travel upwards by $200\sqrt{2}$m (about 283m), the force of gravity will be reduced by half. Each time you extend your ladder's length (or tower's height) by a factor of $\sqrt{2}$, gravity will halve again. Building a tower into space will be tricky, and a lot of effort, but not impossible by any means (assuming there was enough material available). It'd be nice if the builders of the habitat had conveniently provided such things for you, of course.
Orbital velocity at the top of a 283m tower is 22.6m/s. This means that with a relatively streamlined aircraft and a fit pilot you might be able to drive your crank-driven prop-plane into an orbit, and from there you may even be able to raise your altitude yet further until you escape. You might even be able to build a little catapult to get you started. Launching larger craft with more passengers or cargo sounds like a stressful exercise, however. Orbital velocity is inversely proportional to the square-root of the radius, so to halve the velocity required for orbit you need a ladder or tower that reaches up four times as high. This starts getting into the realms of multiple-km high towers that will almost certainly need to be provided by the creators of the habitat, though.
One could tether two worlds together and climb along the framework between them, if the worlds weren't spinning. If they were spinning, you could make a space elevator... the worlds are so small that you could use some fairly simple materials of the sort that would be available with medieval tech (such as silk).
What sort of craft would they use to travel between planets?
Flying around in the void would be easy... a loose framework of sticks and cords would do, with suitable flappy bits (or even propellors... windmills existed back then, after all) and rigging to allow them to be operated by a person. Takeoff with such a craft would be extremely difficult unless you have a very, very tall tower (many kilometres high) so you'll need something much more aerodynamic to get you started. Once you've done that though, you have a means to haul stuff up into space and maybe build yourself a space elevator or staging space station and later flights (and dedicated microgravity aircraft) become much easier.
For landing, you want to be a little bit careful... terminal velocity is likely to be less than for earth, but it will still likely be terminal. Use a parachute, autogyro or glider to control your descent. Docking at a space station would perhaps be simplest.
The biggest problems here, I think, will be the bearings and mechanisms used to drive the fins or props for your aircraft. They'll need to be compact, light and efficient or you'll never be able to go fast enough. You'll either have to have slightly anachronistic machining capabilities, or the builders of the habitat will have to provide space towers. You get to decide which, of course.
edit:
technology up to that of about the 15th century
Ah-hah.
I missed this the first time around but: by the time of the 1400s, gunpowder weapons had been in existence for at least 500 years. Sure, fire-arrows, fire-lances and bombs aren't immediately useful, but again: but the time of the 1400s, military rockets had existed for over 150 years.
Usually when people say they want a medieval technology restriction they forget this sort of stuff, but remember the wise words of Gibson, "the future is already here - it's just not evenly distributed". It could easily be very rare in your environment... it'll be difficult to mine nuclear density matter and do anything useful with it using medieval technology, after all, but a gunpowder Rocket-Assisted Take Off Gear would definately be a way to get your ships offworld.
