While it usually isn't the IG's field of excellence, does Duke Severus still have access to his family's Rogue Trader assets, if any? Does the Git-Slaver maintain a fleet of Roks and worse?

I guess what I am asking is do all of the bad guys have active ships at their disposal? Could they initiate orbital bombardments? If worse came to worst, I could see Duke Severus being beamed out of his throne room, and go on the run in a ship, and could see a group of IG players getting tasked to lead the boarding action of an effort to take out an enemy ship. As for SwFr IG, I assume they are supported, as much as it happens, by Battlefleet Calixis.

Also wonder what a "regiment" built to reflect a force of soldiers seconded to a Rogue Trader might look like. They have the right to garrison troops aboard their vessels, and I can imagine a few Rogue Traders are helping the Imperium on the Spinward Front for profit, if for nothing else.

The Duke's got some Rogue Trader allies, but they try to keep a fairly low profile and focus mostly on supply runs. Technically they're following the letter of any "you have permission to trade outside the Imperium" warrants, but I doubt that would stop Ghanzorik from having them boarded and shot if he found out. He might have a small fleet planned as an escape route, and I could see some ramshackle System Defense ships, but I doubt the Dominate has anything that can really challenge the Imperium's naval power. Just enough ships to launch piratical attacks on the Scarus sector and ferry troops from planet to planet, really.

The xenos, of course, are a different story. The Dark Eldar have plenty of ships, and if the Duke wants something taken out of space that's probably where he turns. And as a planet-conquering Waaaagh!, Grimtoof's boyz have plenty of Meks, and if you keep enough Meks around enough scrap metal, you're going to get a fairly sizable fleet. Probably designed more for boarding actions and transport than extended battles or orbital bombardment (unless the head Mek wants a really killy gun), but they're probably the most significant void-based threat in the Spinward Front.

Most troops stationed on ships tend to use shotguns as their Main Weapon, since there's no real chance of hull penetration and they work well in the close confines of a boarding action. Depending on what they were expected to do or how generous the Rogue Trader is, I could see the regiment being issued with all sorts of other gear, from voidsuits to auspexes. Maybe tech-priests acting as de facto squad leaders for boarding parties (the corrupted machine spirit will be exorcised if you plant the charge at the third cogitator from the left, Trooper Jenkins)

I think you are confusing 'naval armsmen' with groundpounders. Security troops aboard ships a.k.a. naval armsmen are usually equipped with a combination of non-lethal melee weapons and intimidating ranged weapons such as shotguns which are less likely to damage the ship in nasty ways. The whole idea being to either intimidate mutineous/fractious crews and fight off enemy boarders.

Groundpounders are aimed at planetary invasions a.k.a. enhanced business negotiations, and thus are typically equipped as a light infantry regiment by RT players (because they are the cheapest, often the most versatile and capable of defeating opponents with pointy sticks) with a much smaller houseguard unit with better equipment to accompany the RT personally.

I assume that the dominate must have a fleet of some sort otherwise it would probably have been overrun by now.

It however might well be lighter vessels, less effective ships that might have fallen out of more general use and converted merchantmen. Through comerce raiding, ambushes, blockade running and hit and run attacks the Dominate Naval forces could stymie the Imperial Navy. Either the Imperial forces spread out to try to cover everywhere they have to be leaving them at risk of being destroyed piecemeal or they concentrate their forces reducing imperial efficiency making it that much harder for them to win the ground war.

Rogue traders could have any ground troops really. They could be elite house troops equivelent to storm troopers, feral world barbarians and all that is between. I imagine that they might have elite bodyguard units that also operate as special forces, some infantry equivelent to guard and then large numbers of ratings with shotguns, boarding pikes and cutlasses. I doubt they would have much in the way of artillery and tanks but would probably have access to orbital bombardment from their naval assets and maybe a fair amount of aircraft. They could also have alien mercenaries so that would be an interesting element to play with.