I am not sure the U.S. National Archives listens to an inquiry made by a non-U.S. resident.
I'm sure someone there will at least talk to you and tell you what's involved in making requests. It never hurts to ask.
Is there any data prefix I should mention in my request, so they know what I am talking about and looking for? was Apollo data stored under any specific archive name or number?
Here's the rub: the significance of Apollo data being largely unindexed is that it has no cataloging information associated with it. Imagine your [appropriate relative]'s attic. Yes, the National Archives is decades behind and predictably understaffed. Access to unindexed materials is severely curtailed. With any luck you'll be able to talk to an archivist who can, at best, confirm that the kind of information you're looking for is in the collection, because he recalls leafing through it casually.
Do you know if the receiving stations were able to see the telemetry data as it came in from the spacecrafts? I know they could heard the audio and see the live video from the stream. But I don't think they had the equipment to see telemetry data.
The MSFN stations recorded the telemetry, just as did Mission Control in Houston. But of course recording is not the same as demultiplexing and viewing, which would have necessitated more equipment than just the standard telemetry recorders. The difference between the recording done by each ground station and that done in Houston was that the station tapes were just contingency backups. If the MSFN terrestrial links broke down for any reason, the ground stations would be able to replay the missing telemetry once the links were restored. In other words, once Houston had confirmed that it had a block of telemetry "in the can," the ground stations were free to recycle their tapes.
If you could link any documents and files with telemetry date here, that would be great. I guess this thread could be used for that.
Sure, I don't know any specific documents off the top of my head. I just remember seeing the facsimiles after you asked about it. The first place I'll look is the post-flight evaluations of Apollo 13. I recall the discussion of tank pressure, temperature, etc. were illustrated with telemetry strip charts, but that's a distant memory.