When a run succeeds, the rules mention accessing cards one at a time. Does this apply only to the HQ and R&D (in case you have some way of accessing more than one card), or to all servers, as the rules seem to imply?

I thought in the case of remote servers and the Archives, you just picked up the whole pile and decided what you wanted to do with it?

In the case of the archives, the rules say you can pick up and inspect face up cards in archives at any time, and order need not be preserved.

Not sure about remote servers.

On remote servers you can only install one asset or one agenda. Any number of upgrades though so in a remote server you might have installed 1 agenda/asset and X number of upgrades. Turning them over/encountering them one at a time means you have to relate to them in that encounter order so, if for instance, you run into an asset - trap you might be tapped for resources or have your run ended. Or you might spend alot of credits trashing upgrades in the order you encounter them, without knowing if you might want to save those credits for later cards in the same run.

That´s how I´ve read the rules thus far anyways