@ronki23: The only thing mentioned about why Misaki is the Counteractor is that her purpose of existence is being a counterforce to the Choushin's power. You know about yin and yang? If there is something that exists, there is an opposing force to it. Whereas the Choushin seek to create, the Counteractor seeks to destroy all that exists as she serves as a natural opposite to the Choushin. It's about the best thing I can tell you for now since there hasn't been a new title in the Tenchi franchise within the past few years.
As for your other questions...
Firstly,the videos show Ayeka could 'beat' Ryoko
In the OVA episode you have, Ryoko wasn't taking Ayeka seriously at all throughout their fight, which was her shortcoming in getting captured by Ayeka's guardians. I wouldn't necessarily count it as Ayeka beating Ryoko as she would later have Ryo-ohki easily ensnare Ayeka's ship and lead both to crash land to Earth. Also consider their fighting performances against Kagato later on. When Ayeka tried to take on Kagato, she was easily dispatched after just one attack while Ryoko continued to push on despite the pummeling she took from him.
The sample you have from Tenchi Universe isn't a good one to use because Ryoko is much weaker in the Universe and Tokyo anime as she lacks a number of the potent abilities she had from the OVAs like regeneration, summoning demons, breathing in space and no longer having Washu's gems in her possession.
The rest of your arguments seem more like you are nitpicking over why you don't know of certain things to the series and thinking decisions in the storytelling don't make sense since you don't get access to all the information that the Japanese could get direct access to.