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Worldbuilding is an important part of OA, and some of us have made many worldbuilding projects. I have some designs of planetary systems in my personal worldbuilding project, and I am looking forward to enrich these designs in order to add them into OA. Here comes the first system made in this project.
[attachment=2026]
Is this system theoretically possible? Additionally, are there any good names for the star and planets?
I can't really speak to whether or not this system is possible - although we have people here who can and will likely weigh in in the near future.

What I can speak to is another aspect of OA, which is that in the setting the vast majority of star systems are inhabited and developed in various ways.

This leads to the question: Who lives here and what have they done to the place to modify it from its natural state?

Todd
Looking everything over, there are a few minor issues with the system, mostly with the star. Otherwise it's completely fine, and very much possible. Only minor tweaks would be needed with the remaineder of the system, and there are several options to preserve it as originally envisioned.

The Star
The size and luminosity of the star would suggest its on the red giant branch, but its temperature would be much higher if this was the case. Its temperature would imply its near the tip of the asymptotic giant branch, but then it should be many times larger and brighter. Stars aren't exactly my forte though, so it might work as is.

I'd recommend reducing the radius to 60-70 solar, and bumping the temp up to 4400-4100 kelvin to preserve luminosity. This would make it a K8III to K5III somewhere in the middle of the red giant branch, and give an age between 4-6 billion years.

The Planets
Planet b, like other superhepaestians, probably started life as a neptunian and lost its gas and volatiles. It's possible b started as a terrestrial, but it's unlikely given the system configuration. b probably wouldn't have had enough time to make this transition (only starting ~200 million years ago when the star become a red giant). Kepler-9d, with a similar irradiance around a main sequence star, is ~2 billion years old and is less massive. 55 Cancri e, with a similar mass, has nearly triple the irradiance, and is 8.8 billion years old.
To keep it as a superhephaestian, I'd recommend moving b inwards to 0.6 AU, giving an irradiance of ~3400. Alternatively it could be made into a neptunian.

Planet c is quite inflated. Puffy hot jupiters do exist, but they seem to reside much closer in (irradiances ~800+).

Planet f probably wouldn't be rocky. The H2O iceline around the star would move from 8 AU in to 1.2 AU during the first few million years. Its possible that f could have been scattered from the inner system when the gas giants migrated inwards, but it still likely still would have accreted enough volatiles from the outer system to warrant a cerean classification instead. 
Its rocky composition could be explained if it was once an Io-like or Europa-like moon of c, but this seems unlikely given its large mass for a moon and distance from c. While e is closer, it isn't massive enough to boil the volatiles off its inner moons during formation.
I'd suggest making it into a cerean world of some sort. It could have originally been a frozen iceball, but as the star expanded its water melted and eventually boiled, making it into an aquacytherean or aquamuspellian (proposed cytherean subtype with high pressure ices on the surface) world. If it was a bit further out it could be an aquathallasic, aquatohulian, or aquacalidian instead.
 
Nothing is wrong about planet i per se, but the chionian terrstrial type is not currently in use, so you might have to change the name once we finalize the EWoCS. (I'm currently trying to figure out how chionians would fit into the new system, possibly as an arean subtype) The fluid also isn't specified, but it would be too cold for water. carbon dioxide, ammonia, hydrogen sulfide, or methanol could work though.

I would also suggest increasing the eccentricities of planets h and j, as they may have been scattered by the planet g and/or affected by passing stars. planet i could also have a higher eccentricity, but its also fine as it is.

Other than the few minor issues, the system works really well. Hope this helps.
Revised data here:
[attachment=2030]
Change made:
Reducing size of star and heating star to M0;
Reducing mass and semimajor axis of planet b, making it easier to lose volatile;
Shrinking size of planet c without changing mass;
Increasing eccentricity of some outer planets;
Adding laplacian resonance of 2e:1f and 3h:2i;
Other minor changes.
Adding moons and dwarf planets
[attachment=2037]