[Mayday]

I'm not sure if this is already a factor in the game, but I know that sometimes, an empire will have other worlds fracture off from it in rebellions. When you commit genocide on one of these, however, the effect should, I feel, be much worse among the same race than if they were just another alien faction.
I know that if there were another human empire, and some species wiped them out, I wouldn't be very pleased.
Also, there should be a tweak to the AI to encourage recapturing rebelled worlds. I doubt that people would be too happy, if, say, one of the US's states broke away, and the US's military completely obliterated them for it.

Also, again I'm uncertain about whether this is also in the game, but it doesn't seem to be, jettisoning populations into space should be frowned upon. Why, so many times my spies have taken over colonisation ships, or transport ships, and joyfully jettisoned the 'cargo' into the abyss... Okay, well, it WAS me who gave the order, and it WAS hilarious at the time... But still! In fact, it might be an idea to add a chance that the ship's captain will switch alliances for suggesting that he do such a thing. Most people would have some difficulty in pressing a button that would end the lives of possibly billions of people.

Also, I like the improvements to my previous suggestions that people have offered.
In addition to what I said before, I think perhaps the Luminosity value should be used to set the strength of a star. After all, a more luminous star is burning hotter, is it not?

Anyway, as to the point of atmospheric density and worlds being frozen or superhot, or whatever. This also depends, of course, on the atmospheric makeup. CO2 traps heat a lot better than O2. So does Methane. In fact, Methane is 21 times better at it. Hydrogen isn't a greenhouse gas.
Okay, so... for realism this means that we need to take planetary atmosphere density and makeup when deciding whether the planet occupies its habitable band. Obviously, a world with 2 Bar density and say, 90% Methane is going to need to be a lot further out for a habitable temperature than is an Earthlike planet.
So to determine the planet's habitability, we need to find how much heat the star(s) are hitting it with, given its distance out, and adjust this to account for atmosphere with some sort of atmospheric makeup equation.

Also, I'd like to see moons with atmospheres. There's nothing to stop it happening. Many moons in our own solar system have atmospheres, and in any case, you can modify the atmospheres of the moons. Titan happens to have a Methane atmosphere and an atmospheric density of 1.5 Bar.

Regarding Ice planets in Multistar systems, yes, of course they can exist. But they do, as you say, have to be far away. Also, take into account that ice reflects sunlight, so it inherently cools a planet. This is how worlds can snowball. In fact, Earth itself once snowballed. This was undone over time by increased CO2 in the atmosphere, which allowed the world to heat up until the ice melted.

Good grief, I'm going to get a reputation for rambling.

Apart from this, there should be a greater penalty for ignoring demand Messages from other factions. And less of the AI demanding I get out of my most heavily fortified systems. Without some sort of system presence, they don't really have a right.