It is clairvoyance...it's an ability on the Revelation, an Advent capital ship...it can target any planet and allows the user to "see" that planet for a decent period of time...

As for beating the AI, use starbases and level up capital ships/titans...in the long run, you will then have a better fleet than them...

Yeah, it basically is like the All Seeing Eye, but without any negative morale issues. Just ignore it, it's nothing to worry about.

I would recommend learning the game without the pirates. And actually I've been playing this game for years and I Still don't usually play with them on. 

If you'd like to learn in a more relaxed and genocidal environment, I made a sort of custom map for a "Free Learning" tutorial here. Basically it is a map where the AI player cannot ever reach you. So if you have pirates off you'll never be invaded by a hostile fleet (though I recommend you do have them on in this case so you can have some practice defending planets). There are some tough battles to try and give you some combat experience but again, you won't be attacked any more than once every 15 minutes from the pirates, so you don't have any real risk of losing.

You may also find my steam guide useful, or just feel free to keep asking us stuff here.

Best counter to pirates is a trade port....most of the ships will chase around your trade ships, allowing you to shoot them without taking too much damage yourself...