If you have a highly populated planet undefended, a single troop transport could conquer it in the game, especially with a high soldiering. You're telling me that hundreds of billions couldn't fight off a single troop transport?
When that transport can be capable of carrying a number of people comparable to the planetary population, or at least within an order of magnitude of the planetary population even if the target world's population is actually in the hundreds of billions? Yes, I think it's reasonable for the planet to be unable to fight off the invasion. No, I don't think it's terribly realistic that the planet stands or falls in the space of a turn, and no, I don't think that it's reasonable that a single transport with a volume of less than a cubic kilometer is capable of carrying billions of people, and no, I don't think it's reasonable that entire planetary populations can be lifted off to be used for invasions, but those are the mechanics we have. They're silly, but they're what we have.
We could blow up suns in the last game and somehow the supernova annihilated the planets but not the ship right next to the sun blowing it up.
Terror Stars actually do destroy any ships caught within the blast radius as long as those ships are not the Terror Star itself. Terror Stars are also so deep on the magic end of the game's technology that everything related to the Terror Star is so far beyond the reach of the playable civilizations without the aid of Precursor knowledge that it's impossible to build one.
I don't think that your logic about a population of billions being unable to deal with an infestation is accurate
Look, if you take game mechanics at face value, as is suggested by treating the planetary invasions shown in the game as the in-setting actual invasion procedure, you can train and equip the entire planetary population as soldiers within the space of a week without using a single unit of production (bring an empty transport in from somewhere else, land it on the planet, take off with everyone who'll fit into the transport capacity; you have now converted the entire planetary population into fully-trained and equipped soldiers without using a single unit of production from the planet, you have done so in the space of a week since one turn represents one week, and you can use those soldiers at 100% effectiveness without any further delay). If the 10+ billion people on the planet that I can magically turn into fully-equipped and trained soldiers in the space of a week cannot deal with the infestation, then it is not going to be practical for me to bring in enough people to deal with the problem.
If you don't take the game mechanics at face value (because they're ridiculous), then invasion transports are not capable of moving entire planetary populations. Since the largest class of ship in GCIII has a maximum dimension of about 500m, let's assume that our transports are a 500m x 500m x 500m cube. If we do not require any space for the ship's hull or machinery, and we require only 900 L of space per soldier (roughly a casket or coffin), we can fit about 140 million soldiers onto the transport. If we're being slightly more reasonable and instead assume that the troop density is roughly the same as the passenger density within the passenger compartment of a Boeing 747 (very loosely 500 people in 32000 cubic feet), then we're looking at ~70 million troops per ship. If we're actually being reasonable, we could compare it to real-world ships of about the same size and see what they were capable of; RMS Queen Elizabeth and RMS Queen Mary are roughly comparable in volume to GCIII Cargo and Large hulls and carried ~10,000 troops when used as troopships during the Second World War, while SS United States, a similarly-sized ship, was designed to be able to carry 15,000 if used as a troopship. This suggests that if we're actually being reasonable, a somewhat realistic figure for the largest class of troopship I could possibly make in GCIII would carry on the order of 10,000 troops per trip. According to Wikipedia, very approximately 1% of the planet's population are in the military (active duty + reserves + paramilitary forces); it's therefore probably not too unreasonable to expect that about 1% of the planetary population of each GCIII planet is in the military (active-duty or reserves; I'd expect the fraction of the population in the military to be much higher than this during a major war), suggesting that even using the least-reasonable estimates of transport capacity the largest class of transports deliver more soldiers than are already present on even a small GCIII planet, and it's rather likely that you could accomplish at least a similarly great increase in available manpower in a similarly short timeframe simply by instituting conscription at the planet infested, especially if fighting the infestation does not require significant training. Using more reasonable estimates of the capacity of GCIII transports, you're looking at needing thousands of transports per week just to match what the planet can probably expect to gain in manpower through people volunteering or being conscripted.
Having the transports supplying equipment instead of personnel might be slightly more reasonable, but you're still going to run into trouble; high-population planets which are part of advanced civilizations will realistically speaking have industrial outputs at least comparable to Earth's present-day industrial output; consider that in a six-year period, the Allies were able to produce over a quarter of a million various armored vehicles, millions of other ground vehicles, thousands of ships, well over half a million aircraft of various types, millions of artillery pieces, and tens of millions of infantry weapons using only part of the world population of ~2 billion. That's an average of thousands to tens of thousands of vehicles, aircraft, and artillery and hundreds of thousands of infantry weapons per week. What are you possibly going to ship in that the planet cannot produce on its own in great quantities in the same time it takes you to deliver it? Imports might be useful as a stopgap while production ramps up, but unless there's enormously more shipping capacity available behind the scenes than is visible in GCIII (or, for that matter, GCII), it's rather unlikely to be able to contribute significantly to an established planet's efforts to cleanse itself of an infestation (it should also be remembered, before bringing in hidden background shipping capacity, that there is very little indication of the existence of any significant amount of such to be found within the games; a planet's gross non-tourism income is independent of the size of the empire in which it's found, suggesting that there is no significant change in the volume of internal trade as the empire expands from a single colony with a consequential population to an empire of hundreds or even thousands of colonies, and international trade is restricted to perhaps ten or fifteen planets per empire in the known portion of the galaxy and moreover each route is at best worth only about as much as a decent money world or two even on very large maps, suggesting that the volume of international trade isn't that high relative to the economic activity of a planet).
Referring to the xenomorph invasion, the adjectives that come to mind include things like "ridiculous," "ludicrous," "silly," "stupid," and "buffoonish." "Cool" is most notable by its absence. Furthermore, if we're to have a means by which to effectively destroy a planet which can only be used during times of war, I would far sooner have a means of destruction which is reasonably practical, rather than one which makes it appear as though all of the people in leadership positions in advanced civilizations have been replaced by incompetent buffoons who draw inspiration from horror films. If you are going to attempt to render a planet worthless to the various peoples of the galaxy at large, just drop a big rock or a lot of dirty nukes or long-lasting chemical agents on the planet. Simple, effective, much less risk of accidental deployment, far easier to limit the damage to only the intended target, cheaper to develop, probably cheaper to deploy, and certainly less risky to deploy.
Why can't we just nuke the planets?
Who knows? Space-Geneva says no, and even the evilest factions are too scared of MAD to risk it, except when "it" is a Terror Star (although, given that Orbital Bombardment is an invasion tactic, it's possible that nuking the planets, or at least bombarding the planets in ways which are comparable to nuclear bombardment, is already in the game and we just haven't hit the kills-everything-on-the-planet level of bombardment yet)? Stardock's against the killing of entire planetary populations and doesn't want such to appear in their games, except when it involves relatively conventional warfare where somehow entire planetary populations are converted to soldiers in the space of a week?
In all likelihood, infantry will never go out of style for taking over hostile populations. Bombardment is all well and good, but it's only useful if you don't mind depopulating the area, and as long as people are necessary to exploit the resources of a region, simply killing everyone doesn't really gain you anything. Even if you can replace the people with machinery as far as resource exploitation goes, you're still losing out on the tax base, recruitment pool, knowledge, and creativity of the population if you wipe it out.
Furthermore, both the threat of bombardment and actually bombarding an area have historically been of rather variable and often limited effectiveness in pacifying or controlling an area. It's not really going to take and hold ground for you, especially if you place any significant value on what is present in that area.
Why is there a talking squirrel faction?
Talking (or "talking") animals are fairly standard science fiction fare. Star Wars has talking slugs (Hutts) and bugs (Geonosians), sasquatch (Wookiees), teddy bears (Ewoks), squid-men (even in the name - (Mon) Calamarians or (Mon) Calamari), and wolf-men (there was one in the Mos Eisley cantina in A New Hope); the Expanded Universe probably adds just about anything you can think of and there's probably a few things in the movies that I haven't listed. Star Trek has a few of its own and also has a "talking" rock (Horta). Known Space has cat-people (Kzinti). Animorphs has centaurs (Andalites) and mind-controlling parasitic slugs (yerks). Hitchhiker's Guide to the Galaxy makes mice and dolphins into highly intelligent species capable of interstellar flight, and makes both mice and humans into introduced species rather than species which arose naturally on the planet. GCIII isn't that far out there when it comes to weird, silly, or "cool" alien life, what with the seven varieties of humans in rubber masks and makeup plus talking squirrels that make up the eight base-game and one DLC major factions. Things that look like oversized unusually intelligent Earth animals are just not that uncommon or unusual in science fiction.