Point one, precocious six year olds can be like that.
Point two, the whole point is to foster creativity. Formal training in strategy and tactics is actually the enemy of innovative thought, as Sun Tzu points out. A proper study of great generals only seeks to see what they did
wrong, not what "should" be imitated. Imitation is death on the battlefield.
Actually, the Peter/Valentine issue is vitally important to Ender personally, and for Peter to be a pluasible bogeyman for Ender, he has to be just as smart. Likewise, Val--in order to "deserve" the love and trust that Ender invests in her--must also be 99.9999999th percentile. Otherwise, her "goodness" is too easily dismissed as relative simplemindedness. Given the importance that OSC gives to relatively anonymous "nets" in his future society, and the character traits he gives Peter, the world domination part is a no brainer (read Shadow of the Hegemon, it's much better than the other books that you might be tempted to read next

).
Last point. Yes, you're wrong in thinking that it was the "home planet" that Ender colonized. Not only was that planet rendered uninhabitable permanantly, it was the farthest away from Earth (now that, I have a quibble with--why would the Buggers only have expanded
towards Earth?).
The later novels are all quite different. Speaker for the Dead is almost completely about intimate human relationships. Xenocide is all about human evil and why we do the worst things we do. Children of the Mind is...basically a fantasy about how wonderful the universe could be if all the true wishes of our hearts could come true.
Ender's Shadow is sort of a redaction of Ender's Game, though an excellent one. I don't recommend reading it right after Ender's Game if you haven't read any of the other books. Shadow of the Hegemon and Shadow Puppets are all about penetrating the illusions built up around the reasons that nations go to war or make peace. Both are very speculative, but I liked both of them a lot (though I thought the ending of Shadow Puppets was sort of a let down).
Almost all of Card's published works are worth reading in their own right (both from a literary and thematic standpoint). Some of his later work features an overabundance of character introspection (you know, where the POV character seeks knowledge of the mysteries of the universe by studying his navel), but it hasn't ruined any of his books...yet (you should see me when I actually get critical...or maybe you
shouldn't 
).