Your best bet for all the answers is a good reference book about tubes. I recommend "Tube Lore" by Sibley Ludwell.
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Seeing as no one else has answered all your questions, I'll take a stab. Calibration of tube testers is a specialized thing, not just any audio repair shop can do it. I can't recommend anybody for this, you'll have to check out tube sites. Most older tube testers do use tubes for operation, I know most of the popular Hickok models do. I'm sure there are some newer transistor powered units too. There are quite a few tubes still in production, mostly audio related since there is still good demand. Most new production is in China, Russia, and former Soviet Bloc countries. The Soviets used tubes much longer in their electronics than the "western" world, that's partly why they are still made there. Also contributing is the lower cost of manufacturing in those countries. The reason us audio folks (guitar guys too) like older tubes is they were made with higher tolerance and an overall higher regard for quality. High quality new tubes can be made but the cost is quite high and the demand at that price level will not make it profitable. For your final question, tubes will age differently. It's best to use matched pairs when the tubes work in conjuction, such as a push-pull amp, but they can age differently so don't be surprised when it happens. Tube testers are good for keepng track of that (which brings us full circle!). Hope this helps!