In the underbellies of hive worlds and shrine worlds, I imagine quite a few arms dealers knocking about here and there... so hence could be a crucial in stories to do with coups of officials, looking for assassins whom may have used dealers ect ect (more the investigative type of mission) but it brought up a good question...
what is the Imperium's stance on Arms Dealers / Public gun laws? *are there any laws infact?
And hence what would a kill team actually do if they saw one trading in a hive or something similar?

Most of it will be dealt with by the Enforcers depending on the local laws and the Arbites if it would threaten the Imperium, such as selling weapons to dangerous separatists. I don't think that the Imperiums as such has any stance at all but allows the individual planets to make their own laws in this regard.

In regards to the Kill Team they would probably not care for arms dealers unless it was something very specific they wanted. This is the domain of the Enforcers and the Deathwatch has bigger fishes to fry.

I would imagine it would fall under their remit if the weapons were Xenos maybe

Selling weapons without the authorization of the proper authorities is a crime punishable by death throughout most of the Imperium. The said, most criminals are beneath the notice of the mighty Astartes (unless, like Brother Anselm said, xeno weapons are involved; or weapons are being sold to xenos...).

Selling weapons without the authorization of the proper authorities is a crime punishable by death throughout most of the Imperium.

Agreed. However, the 'proper authorities' is a Planetary Magistratum (who'd define 'gun ownership' laws) and/or (at MOST) Arbites level (if the weapons were identifiably 'Imperial Manufacture' - stuff like bolters).

Gun ownership will vary from world to world but according to Dark Heresy packing laspistols, light blades and similar sidearms is acceptable virtually anywhere - certainly a Civitas laspistol is almost 'normal' on a lot of worlds. Downhive and frontiers, small arms are equally acceptible, and hence weapons dealers dealing in them will be equally so.

Uphive 'noble' gun-dealers, making things like custom hunting and duelling weapons, are also fairly common and several have been named.

Essentially, unless specifically related to the kill-team's mission, a kill-team would probably ignore a gun dealership (even if probably illegal) unless:

1) They have reason to believe the weapons are being used to arm the kill-team's targets.

2) The dealer is dealing in massive quantities of weapons -we're not talking a backstreet shop but a warehouse full of heavy weapons and ammunition.

3) The dealer is dealing in xenotech or archeotech

4) The dealer is dealing in highly sensitive imperial (especially astartes) technology. Bolters are pushing it, but broadly acceptible ('rare' on a planetary scale means little to the inquisition and its agents), but if a kill-team were to find a gang-fight corpse during an op that had clearly been killed with Angelus-calibre bolter shells that are supposed to be made only by the mechanicus directly for the marines, honour would demand they investigate.

That's not to say they don't give a **** about planetary law - the more civic-minded marines would probably inform the magistratum/arbites about the weapons dealers post mission completion - but it's not their job to deal with it and theoretically not their jurisdiction either.

Not that jurisdiction means much to (a) someone assigned to the Ordos and (b) someone with the firepower of a guard regiment at their disposal, of course.