Right, let's look at the floating islands issue. Are they unusually buoyant? (Or, come to that, is the atmosphere unusually dense?) Repelled by whatever it is that keeps the shell of the planet (if it so possesses one) from collapsing? Are the held up by the same mysteryforce that counteracts the massive gravity at short range (i.e. not as far as the sun, but also ensures that the several-hundred jupiters of mass doesn't crunch down into a brown dwarf, or worse a neutron star[1]), either in conjunction with the above or due to 'leaked' localised resonances that sustain (and carry) 'pockets' of rock, and whatever lies above.
Superconductivity/magnetism 'maglev'? Whatever it is that happens in Avatar/Transformers Beast Wars/etc with an exotic element? Naturally-occurring Cavorite 'ores'?
How about... A whole lot of massively strong banyan vines/similar attached the the rock, with (for example) helium or (perhaps easier to create through biological processes) hydrogen in massive balloon-'tops'. Used by the plant(s) to out-compete neighbouring plants in the search for light, particularly abundant stands of vines upon certain rocky areas prosper
so much that, having integrated themselves into soil and even rock below them, their oversized lifting 'buds' generate so much force that they've
ripped huge swathes of the land beneath them out of the topmost later of the very crust itself of the planet itself.
(Now imagine someone bursting/igniting those balloon-buds. Especially the latter, with the chain reaction along the whole set of balloons, and no "softly settling mountain" to worry about, because it's probably too late to worry if you're beneath it when it happens.
)
Yes, and Magic, disguised as Handwavium as required.
Apart from the (possible) lift-vine population, fauna and flora upon the floating mountains? Well, avian life of some kind, obviously. (Includes bats, pterosaurs, flying insects (massive ones, probably, at least as the more obvious ones), and anything else with powered flight. Just like a rocky island in the middle of the ocean, it might be the sanctuary/breeding place of a given species (or several) of the active fliers. Each 'flying-island-mountain' might have its own population(s) and when onverging air-currents contrive to draw such mountains together there may be 'territorial' conflicts over the intervening airspace, and the 'penumbral' hunting grounds planetside.
(Doubtless there'll be specialised underside-dwellers, although if there's any risk of the mountains 'grounding', probably very nervous ones living quite close to the edges.)
If we've already got floating mountains, doubtless we also have floating creatures. Either intrinsically blimp-like themselves or commandeering the lift-gas or lifting-buds
themselves. Floating more easily on air currents (and perhaps using intelligent vertical control, as well), they'd probably intercept the mountains that are subject to inertia as well as winds. Perhaps they'd breed there (and grab some more gas/bit off more buds, if necessary?). But they'd be lower in the food chain than the active-flying residents (unless significantly large and whale-like, perhaps).
Plants... well, as with island plants, so with floating-island-plants. Although they may more readily disperse seeds to the air to land on other floating islands (or the ground below; probably to be grazed to death as shoots, however...) The more the floating masses are transient (potential to fail and fall, new ones arising periodically) the more migratory/'dispersary' the residents will be of course, but if they're permanent features you'd probably find fairly insular (ha! literally!) speciation.
Intelligent beings will almost
certainly attempt to get onto them. I can't imagine there not being a civilisation or two that has staked its claim (however transiently) upon such a prize. Whether climbing up ground-dragging dangling roots, hitching a ride (intentionally or not) upon a new upstart floaty mountain or developing/hijacking the power of flight for themselves, as individuals. If there
is such a thing as a long term island-in-the-sky, it'll doubtless have temples (or a cultural equivalent) carved out in its rocks, even if abandoned (or not apparently of the current inhabitant culture... say like Amazonian Indians clambering of Aztec temples without much care what they are, or at least interest in maintaining the 'Caves Of The Gods'). If we have tech-savvy inhabitants, maybe there's something they're doing (or trying to do) to
steer their home-mountains. Out of necessity or to a purpose such as warfare with other 'floaty-island-states'. If they are
not technically capable, then they may still be ritualistically attempting to influence matters through their gods, etc. (What would be interesting is if there's a mix, either new "rationalist" members of the society have developed the capability even while it remains superstition for the remainder, or a prior technically-able culture has left behind remnants of the tech and its control panels that are (knowingly or not) used by the priesthood to 'worship' their way around the world, to whatever end).
Should controllable flying mountains be a reality, then ground-dwellers are probably subject to those flying them. Tributes to be paid to ensure that their shadow of 'eternal' night[2] is cast down upon some other poor blighter's settlements/territory. If they (or enough of them) remain uncontrolled, then there's pot-luck. Probably encourages nomadic lifestyles, ground-side, or at least territories featuring a number of "alternate" home bases, garrisoned and maintained by volunteer troops (even while under a shadow) so that when the current 'capital' is threatened by shadow
If the mountains are in
fixed aerial locales (not subject to the winds, perhaps just stuck in a resonant "lifting force" area) then we'd be talking permanent areas of darkness (although.. sun-rise and sunset would, at the very least, creep in under the edge to most of the enshadowed area, making it more a place where the sun
rarely shines), with dark/twilight-adapted populations perhaps occupying these areas. Temperatures would be
barely below the surroundings (a few degrees, but wouldn't make a temperate zone arctic in nature, for the size of shadow-casters I'm thinking of, but Ym
2MV) but would definitely not support the same plant-life as in the open. A transitional zone of shade-lovers merging into non-chlorophillic plants? A potential for the clichéd "large carnivorous, semi-motile thorny-vines", and some-such. Mushroom Town a possibility for the other. Think of where the nutrients are coming from. (Rivers washing through a zone might be a good source of organic material.)
I'm somewhat minded to imagine there'd be giant ants/similar, farming mushrooms and occasionally raiding neighbouring 'non-nightside' settlements (or ones only marginally under the shadow above) for protein (cows, normally, but perhaps people too if they aren't too disadvantaged in the weaponry stakes and don't have their own morals against farming the
farmers...) for themselves or various organic stuff (again, with varying possible prime targets) to set the mushroom crops atop.
If not them, then all kinds of 'normal'[3] outcasts could use this zone as a 'badlands'. By choice or exile. (Alternatively, a twilighter-race could exile
its undesirables and inconvenient-heir-to-the-throne-people to the unshadowed landscape, probably to be treated with suspicion and/or awe, if not open hostility. Reverse that as necessary for a good socio-political setup.) Pale skins, the tendency to squint etc, and/or their tendency to wear heavy clothing against the sun, would mark such exiles out, whenever roaming the 'outer lands'.
By the way, sorry... but I've a feeling you want something solid rather than "we could do this... or
this, or maybe
this... and we can do that as well, perhaps with a bit of
this..." If so, feel free to pick and choose, because right now I'm just seeing a whole lot of different possibilities and having a hard time nailing myself down onto any particular one.
[1] Not sure about that. Jupiter is 1/1000th the mass of the Sun, and you're looking at at least 1.4 solar masses (thus 1400 Jupiters) to make up te smaller neutron stars. Although the advantage is that if it's a less fusion-ready set of elements (iron+, especially) it won't have that additional residual 'pressure', nor need to "blow off" so much of the top mass in order to drive the deeper mass down.
[2] And threat of settling down? ...however practical that might be, possibly being catastrophic for the island if the bluff is called and it is
attempted!)
[3] i.e. human in a human-settled area, but switch and swap for the various actual races this planet is
actually going to be supporting. Consider humans as a shortcut tern in this example, and anywhere else I've inadvertently mentioned them.