Here is a link to my completed ships [imgur.com], I am hoping to pack a similar level of detail into the Inkling one.

Managed to swap the palette on the existing FU BYOS ship parts to match the Inkling ship[imgur.com], never worked with sprites at all before so I'm glad it actually worked.

Now I just need to figure out how hull paneling is sprited so I can get something custom going there too, nothing is a good enough match at the moment.

Edit: Current Progress[imgur.com]

Hey, only just found this and this is probably a pretty cool way to talk about this.
To answer your initial questions--

Inkling living spaces are pretty varied depending on where they live, but it does follow patterns. They seem to really like urban areas, and when living in them, they keep small, decorated living spaces in apartment buildings. They're a very social race so having sort of "small personal space, large communal space" type deals is a thing; it's weird to see just one of them alone, which I'm trying to reflect in future microdungeons.

But you also might find some Inklings that, if they have the money and resources, have bigger and more decadent living spaces. There's at least one character whose family owns a mansion, and many more who could probably afford a fancy penthouse or other fanciful lodgings if they wanted to.

Fashion over function is 100% their thing if they can get away with it. Being cool and hip and with the times is a very Inkling desire, they want to try their best to stand out while being as fresh as possible. A low-tier ship might be more functional, but a higher-tier ship might be more showy. Showing off one's personal style is a big deal for them! Recreation space is important because of how they value fun and leisure time, especially if that recreation space can be outfitted with fun decorations and objects.

In terms of decorations, almost anything goes. Inklings like to "borrow" decorations, structures and designs from other cultures and mix it in with their own aesthetics, which vary from colorful and upbeat and fun to grungy and industrial to quirky and varied.
In Starbound specifically, they have good relations with the Hylotl and have a fair bit of cultural exchange there; they also like the fun colors and energies of (non-Stargazer) Avian decor and Human inventions. But it's always arranged in a distinctly Inkling flavor, things are always colorful and fun and never free of bad sealife puns.

Having pool/s of saltwater wouldn't be unusual, because they /are/ squid people who need to keep things humid for their health. (Their pet sea slugs also like this.) They're rather sensitive to water quality, too, and like their water untreated with chemicals and without pollutants.

A small greenhouse also wouldn't be weird. They're obligate carnivores but regularly eat a lot of other things mixed into their food-- rice, wheat sugar, and various fruits are all pretty common. While an Inkling can totally live off of canned sardines, they're not going to be particularly happy about it. They need high-calorie treats and eats to be at their best.

That current progress on the ship looks pretty fun! The color choices fit well and I really like the little glass area where you put SAIL. It's definitely along the lines of "fun but functional" that I can see Inkling ships being designed around.

Right, so I have the bridge in the dorsal eye and an 'observation pool' in the ventral eye for a place to relax in the water. FU actually adds saltwater to the game so I can fill it with that, i added the colourful pole so the nudibranch could actually climb out of there again.

The dorsal nacelle has a firing range rigged to a pressure plate at the barrier to switch the lighting and close the door. I might add some more tech decor to the ventral nacelle just to fill it out a bit, FU adds a bunch of functional ship parts (like the fuel tank there) that can replace the decorations as a player progresses. The FTL drive and fuel hatch are where the beak should be, roughly.

The upper deck I am intending to leave mainly open, so a couple crafting stations can be placed without needing to tear out all the furnishings. The middle deck is just packed with recreation and a functional crew member bed (in FU BYOS you unlock crew member slots with functional furnishings). The lower deck is all crew amenities, with a kitchenette and bathroom.

The overall ship lighting I kept relatively low, I dislike having excessive light spill or areas completely washed out with light. Much of the light is actually produced by tiles and liquids which glow[imgur.com], the thruster mounts actually have liquid erchius over the top of erchius crystal for a constant purple light.

I'll have a dig through some of the vanilla assets to see what vibrant and quirky items I can add that an Inkling might have liberated on their travels.

A firing range is a really swell idea, as is an observation pool! The ship lighting detail works out well, Inklings looooove anything that glows or twinkles. Fireworks and glowsticks are a pretty big mainstay in their celebrations, and squids just... like light, lol. Any tech-y glowing doodads or lights or buttons seem like they'd be popular in ships for that one reason; that's one reason why I picked the Hylotl ship as a base for these guys, along with it just being familiar to them.

Definitely post more links for pictures as you make progress, I'd love to see more.

I realized that I forgot to address this bit here.

> How likely are they to furnish an engineering area and hang out there?

I'd imagine any workspace would be as personalized as the rest of the space they call their own. It probably won't be neat and tidy-- they tend to tolerate mess and clutter if it's "their" mess and clutter.
Engineering isn't the hugest Inkling thing, culturally; that distinction belongs to their octopus cousins. But I imagine any squid with a spacefaring ship will /probably/ have at least some interest in the art of making stuff... or they might have friends that do!

Alright, I've updated the progress pictures.

I managed to squeeze a small agriculture space into the ventral nacelle, has enough clearance for all the hydrophilic crops though there really isn't much space for regular crops without alteration.

Added some greebles and adjusted the furnishings and decorations to be a little more diverse. Observation pool has a sound system now, rigged to a lever in the water.

I'm pretty happy with it overall, I'll go learn how to package it all up into a functioning mod.

Let me know if there are any specific changes you would like to see, I'm happy to accommodate.

Hey, that looks excellent! What a fun ship, the residential areas are very nice and I'm really enjoying how much space you managed to decorate. The little agricultural area turned out good, too-- I'm adding another hydrophilic crop in the (eventual) next update so it works out! Big fan of all the details, even just the modern stools in the observation pool, the chair near the agricultural spot, and the very-neatly-fit Squid Friend next to the crafting table.

Once you get it finished and uploaded, I'll link it on the main mod page!

One handy thing I noticed playing with the new ship is that NPCs don't clutter up the bridge and get in the way of your chair, probably because there isn't anything else up there to mess with.
While they won't sit in the observation pool due to their AI being liquid-avoidant, they do however dance in the bathroom, because the speakers are technically beside it.

Amusingly while testing the firing range my nudibranch came in and fell asleep on the pressure plate, trapping me in there. I set a custom parameter in Tiled so it will only trigger on players, but was funny for a minute.

Did you have any ideas for graphics to use for a preview image? I have some Frackin Universe logos but besides that I'm not really sure what to include.

Swapped out the FU tilesets to make an independent version so you can view it in Tiled, added preview to the progress imgur[imgur.com].
I'll just include it in the .pak without any dungeon to actually generate it.

I think dancing in the bathroom is entirely on-flavor for this ship, it's just a whole party experience. That's pretty funny about the nudibranch too, what a little prankster...

I'm fashionably late (again, it seems; I've been very busy the past few days!) but the preview graphic you posted in the main comments looks pretty good!

I've now posted the addon, feel free to close or hide this discussion if you feel like it.