Multiple tech-requirements do work. I've tested them myself. Make sure, that you are using the correct name of the tech (the ID, not the DisplayName) and that there are no typos. If everything is correct, then you should see your tech appearing behind all of its prerequisite techs. That's only a UI glitch (the Tech Tree UI isn't set up for this). It doesn't have any other affect.
Also, where did you make your changes? In the TechTree.xml, or in the RaceName_TechTree.xml of the race your working on? If it is only the former, then there could be something in the race-specific tree, that is preventing some of your changes to show up. The race-specific tree takes priority over the TechTree.xml.
The Category-tag tells the AI what kind of tech it is dealing with, and influence its research decisions. There are several other tags that influence the AIs research too, like the Tech Branch (Culture, Industry, Weapons, etc.), the Cost, and the AIValue.
One last thing, to prevent any confusion. In the modding community, the Tech Branch is called ID, while the actual ID is usually called InternalName. No idea, why that is, but it has been the case for as long as I remember.