1. Kakashi only found out in a later fight with Obito that the dimension that the objects Kakashi warps, and Obito fades in/out of, are the same. Which is why he never did that.
2. That Chakra usage man. Kamui at that point would kill sir Hatake after a few uses. Let's not waste them.
3. Jiraiya's form wasn't perfected. Earlier in that fight, the frogs on his shoulders were yelling out if the Pein's got behind him. He probably couldn't sense chakra.
4. Yes Hiruzen is an A$$ who does shady $#!T, but he always seems to have the idea in mind to make the Leaf better. Hiruzen doesn't like getting his hands dirty, why not have someone under you who does? I don't like it either though.
5. I don't think he wanted anything to go wrong. If she were to die, he would lose his chance to control the Kyuubi at that moment. He'd have to wait some time when the Kyuubi would uh... "spawn" again lol
6. Idk why he doesn't use mokuton, maybe he just prefers what he's grown up with. In that little blood rage he went into when Rin died, I don't even know how he just knew he had mokuton. Maybe he forgot. but whatever. During the fight with Minato, he was probably so in shock that Minato landed a blow, that he just forgot entirely to warp him. I mean, he caught Obito off guard with the Level 2 FTG. Idk..