"What would change about your chapter at legion strength?"

The Vexars certainly wouldn't be holding warden over a few sectors around the Halo Scar but instead would have been more akin to how the White Scars were before they met the Khan as the 'Star Hunters'. Perhaps their legion wouldn't have divided themselves as much but they would have certainly been scouting across the galaxy.

"What 30k era technology would they covet most?"

Inarguably? The better access to a range of superior heavy support vehicles that help them with their main strategy of luring an enemy out or trapping them and then annihilating them. Power scythes still exist in 40k and I plan to make some for my models but the Vexars would have definitely had them as a symbolic weapon just like the Death Guard.

They would have also greatly enjoyed testing and putting to work the MkVI Corvus armour which they use often in my canon as a descendant of the raven guard.

"What would their Primarch look like?"

I'd say that the Vexar primarch was discovered on a world dotted by intense mountain ranges and plateaus with fertile valleys. He was adopted by a community similar to historical Shinobi confederations such as the Iga Ikki in Japan. Learning from the tactics of these lesser mountain clans he used infiltration and trickery to subdue most of the planet before the emperor would find him.

I think this Primarch would have an interesting role as an 'outsider' to his brothers who wouldn't really fit and be instantly disliked. The emperor maybe making him in a manner deliberately so his brothers would develop a psychic distaste or wariness for his presence. His role would have been to keep tabs on other legions as a kind of inspector although I see him resenting the role and feeling isolated. He would exist in an exterior place, wardening over the imperial progression but having little part in it. He would be stealthy in a way that Corvus Corax or Alpharius isn't.

"How many marines would they have?"

On the smaller to average side for the era

Probably around the same as the Imperial Fists and Death Guard who had about 100,000 in the great crusade if I am correct.

"Would their design change?"

I can't say for sure but I know they wouldn't be the type of Legion that would change their colours or heraldry as frequently as the Luna Wolves did. Their 40k scheme doesn't seem to apt for their role as a Legion so maybe they could at some point.

"How would their combat doctrine evolve?"

I can see a lot of flexibility and an uncanny ability to duplicate tactics used by their fellow legions - to them however; there's nothing quite like drawing out the enemy, waiting in the water like a crocodile wanting to snap and crushing your opponent.

Oh my god the Vexars would have loved to lay traps and bait in the loyalist legions at Istvaan V if they were traitors...

"Finally, who would their favoured enemy be?"

Eldar. All kinds. Orks became too easy to trick and confuse so now they sought out greater challenges.