A right-handed Jedi (or Sith) using a single Sabre should carry it on the Right hip, but draw with the Left hand. REAL Swordsmen always wear their blade on the opposite hip, and draw across the body, but that's primarily for one-handed weapons. If you're going to use both hands, you'd draw with the off-hand, and leave the upper section of the hilt open to great your main hand as they come together, and you "ignite" it with your main hand. Also, note that the animations for the Marauder and Sentinel show them cross-drawing both blades.
I'm not totally sure I understand your post, but I have considered drawing with the off-hand and then placing the dominant hand on top. However, it would be hard to quickly attack or defend by doing this, whereas if you only used one hand to draw, you could attack/defend in the same motion.
Incorrect. Virtually all lightsabers have a button, switch, or activation stud; however, they are almost always hung from the belt in such a way that the activator is less likely to be bumped to the "on" position. As to the second point about deactivation on death of the wielder, my theory is that most lightsabers require constant pressure on their activator to maintain the blade, or have a mechanism to "lock" the blade - for example, when the weapon is to be thrown.
I think having a locking mechanism would be useful, though it would mean one extra step when turning the lightsaber on/off. I personally wouldnt want to keep constant pressure on a button the whole time though. One idea I've had is to get rid of buttons altogether. Given the fact that Jedi are able to activate their lightsabers with the Force, they dont really need a physical external button to use them. Perhaps they could have an internal button that they could trigger with the Force when they need to, thus solving the problem of accessibility.