Can non-rule-specified items be used to mark information that is shared but closed?
Is there anything that disallows or allows or even requires markers to be used to indicate which of a group of facedown cards previously had a particular identity?

A player must ensure at all times that their face-down spells and permanents can be easily differentiated from each other, but a physical marker is not necessarily required to do so. If just one card needs to be tracked, its controller could say &quot;I'm going to keep the one you've seen on the side by itself.&quot;

707.6. If you control multiple face-down spells or face-down permanents, you must ensure at all times that your face-down spells and permanents can be easily differentiated from each other. This includes, but is not limited to, knowing what ability or rules caused the permanents to be face down, the order spells were cast, the order that face-down permanents entered the battlefield, which creature(s) attacked last turn, and any other differences between face-down spells or permanents. Common methods for distinguishing between face-down objects include using counters or dice to mark the different objects, or clearly placing those objects in order on the table.

(Emphasis mine.)


Even further, is the player allowed to place markers on cards under the opponent's control to assist in tracking these previously known identities?

I can't find anything that would allow this serious breach of gaming etiquette in the rules (Comprehensive or Tournament). People can be very picky about their physical area of control, and that should be respected.
If the identification is truly unclear, you may request that the identification be made clearer (bringing in a judge if necessary), but you can't mandate the use of a specific scheme.
If you are having problems keeping track of everything, keep in mind that you may take notes.

2.11 Taking Notes
Players are allowed to take written notes during a match and may refer to those notes while that match is in progress.