I've already posted the premise on the ASB thread, but this thread seems more appropriate:
A K-type main sequence star, 0,5 times the mass of the Sun and a surface temperature of 3.900 K.
0.5 solar masses fits more with an M1V-type star; the smallest K-type stars will be around 0.60 solar masses.
Some stats for the star (with 0.5 solar mass, 3900 K):
It should have about 6.61% the luminosity of the sun (=mass^(3.5)).
The habitable zone should extend from around 0.24 to 0.35 AU from the star, using the 0.95-1.37 estimate for our own solar system which is most common - proportional to the square root of luminosity.
The star's radius will be roughly 0.60 solar radii.
Near the center of the habitable zone of this star,
You may want to go a little further in with this; Earth is near the inner edge of the Sun's habitable zone, and you don't want to interfere with the stability of the other planet.
a rocky planet with a mass 2 times that of Earth, with a radius 1.3 times that of Earth;
This is just slightly denser than Earth. It will probably have a smaller core. Gravity will be 1.18 g (=m/r^2).
the atmosphere is richer in oxygen than Earth's, but nonetheless very similar to ours - it'd resemble the atmosphere Earth had during the Carboniferous period.
Around 35% oxygen, then.
The surface would be covered by a shallow ocean peppered with several flat island chains.
Sounds like there wouldn't really be much height variation. The planet would then probably be less geologically active than earth.
Near the outer edge of the habitable zone of the same star, a small rocky planet with a mass equal to 2,7% that of Earth,
This is quite small - just a little larger than Ganymede. The star is smaller too, though, so I think it would be able to clear its orbit. It could be difficult to maintain stability with the narrow habitable zone, as I mentioned earlier; perhaps set up a resonance between the two planets.
and a surface between those of Ganymede and Mars;
what do you mean? in terms of temperature? composition?
despite its small size, being more distant from its sun might allow it to retain liquid water and a thick atmosphere,
Being within the habitable zone, it should definitely be able to hold liquid water. A thick atmosphere is also definitely possible; how many atmospheres do you mean?
leading to it being a low gravity water world;
Given your mass, for a water world (specifically, a world where H2O covers a large fraction of the planet's mass), according to
my reference chart (figures 4, 5; pages 21, 22), the radius should be between 0.33-0.45 earth radii. Err on the lower end of this for a larger core and silicate mantle, which I think you'll want for habitability.
life could almost float in water and sky alike, and perhaps land-based life could colonize continent-sized chunks of ice,
Sounds cool! The continent-sized chunks of ice will probably take the form of polar ice caps which shrink and grow yearly (assuming you have seasons).
if actual land is scarce.
Actual land will be nonexistent on such a world.
Both of these planets would have moons of their own, to help with tides and so on,
Makes sense. This is rather unlikely for terrestrial planets; there are only 3 moons, and only one major enough to cause tides, out of four terrestrial planets in our solar system. However, tides are likely important for habitability.
and several gas giants on the outer edge of the system could protect them from asteroids and comets; lifeforms would be squat and stocky on the first planet, that would have a higher average temperature than Earth,
Maybe add a bit of a greenhouse effect to ensure higher temperatures, or else keep the planet close to the inner edge of the habitable zone.
but lanky and spindly on the second planet, that would have a lower average temperature than Earth.
Would it be beneficial to be spindly, on a world where heat loss is a major concern?
Would such a system be plausible?
Seems pretty plausible overall to me.
A different plausibility check that I've been thinking about for a while for a fantasy-esque idea. Could a star system's barycenter be stretched out far enough to be located in the star's habitability zone? And if so would there be any gravitational side-effects for an object located there?
You mean like, a multi-star system? It's possible for the barycenter to be in the habitable zone, but if you tried to put a planet at the barycenter, it would have a very unstable orbit.