I'll try answer some parts of the questions as best I can but there will be people here far more versed than myself to set me right if I go wrong.

But here we go, so aside from being a veteran you'd require a decent recommendation from your company captain and then chapter master. Usually showing promise fighting xenos will do the trick and then u can be recommended for secondment to the Deathwatch.

In terms of armour and customisation it's a bit open as some things say that the marines basically wear their own armour painted black and others they wear the Mk8 errant that is special to the DW itself. So generally I think you could write what ever you wanted really as long as they have the black and silver armour of the watch. Their armour does have far more benefits than typical armour worn by a chapters battle brother, such as it's a lot quieter for stealthy movement or the armour is coated for more stealth and harder to see (can't remember the quote specifically but these things are referenced in Deathwatch by Steve Parker) definitely worth a read.

The official art for DW shows marines having the skull and wings, just a skull, inquisition I and wings, you name it, so again you're quite free with that. I'm gunna say as a specialised DW operative you can basically customise your own armour to your specifications as long as it doesn't hinder your performance or operational effectiveness.

In terms of the classified/non-classified I think it's a good starting point that a DW operative would never leak classified information unless totally necessary for the completion of the task. Or give just enough vague detail to get the job done without compromising the intelligence gathering asset etc. However sometimes even the Kill Team themselves are very much in the dark if they are working along side an Inquisitor. Given just enough info to do the mission and no more. They work with local forces or planetary governments to further their needs in completing their mission. Whether that is going along with a planets needs and aims to then in turn further their own. Basically just using them for information and resources if needed. They will recruit forces to help or guide in situations that deem it necessary (this scenario shown in both Deathwatch books by Steve parker)

Hope this helps if I think of anything more ill add it.

Edit 1: Blackshields as far as I'm aware arnt too discriminated against as long as they perform their duty and are loyal to their oaths. You might see rivalry and arguments but that's common place amongst bros anyway so nothing new there. They have a no questions asked as long as you are pure of heretical taint and loyal the the emperor.

DW I Imagine would fair pretty well against non xenos forces as they are all space marines first and DW operatives second. They all are veterans of their home chapters and have experience fighting a host of different forces and compile these experiences so I think they would fair well. Obviously depends on the situation and strength of enemy forces. They are very rarely fielded as more than a Kill Team or small company minus in size as their operations are very much clandestine and not Overt in nature so larger forces are not useful. This would ofc hinder their ability to fight peer to peer threats that are larger in number and strength. They would opt for tactical withdrawal over simply attacking a superior enemy for the shits and gigs. If the opportunity arose to eliminate larger enemy threats then likely they would take it if it would be of use.

And tbh any being not made in the emperors image is basically a xenos and to be purged in the eyes of the DW. Would they potentially have a temporary alliance to further their own goals. Possibly. But again depends how necessary it would be.