Hey guys, I'm one of the devs working on the stats right now. I'll answer a few of your questions:
A search is coming, you'll be able to search for a player's name and it will return all players with that name (or similar) along with their rank and some other information. I'm also looking into allowing you to search by PlayerID or AccountID (PlayerID is an in-game ID used by Demigod, AccountID is your Stardock Account ID).
The reason some of you see your names twice is because you may have multiple PlayerID's. It was decided that multiple players will be treated as different people statistically rather than as 1 player. This may change later.
The design is unfinished. Once I have all of the stats up I'll likely give it to our design team to finish the job by making it look a bit more interesting. I still plan on adding some graphs, charts, and a few graphics here and there, but I'm not a designer, so it probably won't look amazing 
The way the ladder is setup at the moment may not be representative of the final game's ranking system. It's only one way of ranking people and may change by the game's launch. We will take feedback on this ranking system into account when developing it further, so feel free to continue sharing your thoughts.
That ranking glitch gnats3 pointed out is new to me. We'll look into it further this week.
As far as AI players are concerned, unfortunately that is not up to me. But again, user feedback will be taken into account on this matter as well.
Keep your suggestions coming, I'll try to implement whatever I can in the coming weeks 
Bara