The Outer, Earth Like Shell
If you make the outer shell thick enough to create magma using the same method as our own world, then the outer shell will be so thick and fluid that the local gravity with overwhelm the gravity of the black hole causing it come apart and form planets. So, you need it to be too thin for gravity to be the source of its magma layer. That said, there is a second source of heat that contributes to our plant's molten core, and than is nuclear decay. If your shell contains a significant amount of fissile material, then you can melt a silicate layer even if the shell is relatively thin... but in doing so, you must ensure that the inner part of your shell does not melt because if it did, then gravity would pull it apart.
So to do this, your outter part of the shell would mostly be Silicates which melt at 600-1200°C. Next you need a thin layer of something too hot to melt like Osmium or Tungsten that melts at about 3400°C to keep your fuel from mixing with your silicates... otherwise, your volcanoes will be extraordinarily radioactive. Next you have your fuel layer, probably some mixture of molten salts and a fissile fuel source like uranium, plutonium, thorium, etc. The salts will keep the fissile fuel from going critical, while the the fuel will create the heat that conducts through the outer tungsten layer to melt the silicates. So this layer will need to be somewhere between 1200-3400°C... probably closer to 1200 is best. In this way, your shell could conceivably be only 10-20km thick (plate tectonics will make sure that this number is variable depending on where you stand). Not nearly the thousands of km required if relying on gravity pressure to heat your mantle; so, local gravity will not cause the shell to break up. Lastly, you need an inner tungsten layer to keep your molten radioactive salt bath from spilling out onto the inner shell. This layer will also glow red-hot providing 24 hours of artificial light for the layer below.
The Middle Firmament Like Shell
With all that light radiating off of the bottom of the outer shell, the 2nd shell needs a lot of help to be a habitable place. An entire sky, glowing at 1200°C will make the surface temperature of this shell very hot. The main purpose of this shell will be to reflect heat back into the outer shell reducing fuel consumption and blocking the heat from reaching the inner shell. Since the outer shell can absorb more heat via conduction + radiation where as this only gets through radiation and maybe a negligible amount of convection, it should heat slower than the mantle, but it will not actually be able to passively stay cooler because trapped between 2 shells, there is nowhere for the heat to go. So, this layer will need some kind of cooling system that exchanges heat back up through the outer shell where the heat can radiate off into space.
To do this, you need vents in the outer shell to create a convection cooling system. The Middle Shell will be covered in oceans that will boil from the intense heat, that steam will form cloud that will move up to the surface vents releasing clouds that will radiate the heat off into space. Those clouds then rain down to fill the top layer's oceans that then pour cooled off water in great waterfalls back down onto the second layer.
While the surface of this ocean will be boiling hot, the deeper you go, the more it cools off; so, you could still have a massive aquatic ecosystem here. The other interesting feature this shell has is that it will act as a filter, allowing some of the radiated heat from the 1st layer to reach the 3rd layer. So with great windows, this layer will act like the Greek idea of the firmament: a sky with windows that lets in just enough light through holes that create the "sun" and "stars".
The "Dark" Inner Shell
While the middle shell will let though enough heat to make the 3rd shell comfortable to live on, it will all be infra-red light. Not a good place for Earth like life to thrive, but any organism that evolved to live around a dim red or brown dwarf star will feal quite at home here.
Why Build such a wacky world?
While each ecosystem is unique, they could each support life the evolved in very different ways. This "world" could be the capitol planet of a massive 3-species alliance where no species can live on the same kind of world, but this lets them all live in very close proximity to one another.