I intended to reply on Tuesday night, but lost the relevant text.
I believe that this is a cause and effect universe, but not every event that has ever happened is intertwined with each other. My decision to buy a can of Pringles will not affect someone in Russia facing the same choice. It might though, if I bought the last can of Pringles in the store, which would prompt the owner to place an order for more. The supplier would then ship them out to where I live, rather than where they would have gone originally: Russia. Now, the Russian man has no Pringles to buy. Or perhaps because the restock didn't come in time, he doesn't want to take one of the last cans simply because he's feeling peckish. In that case, my decisions do affect others around the globe.
1. You are obviously a man of science. Science tells us that sensations are passed through the nerves to the brain for processing, then sends the appropriate signals and response back to the affected area. I believe that the hot surface does actually cause you to feel the pain, through a microscopic game of telephone. There are people who cannot feel pain, which is also explained through science. We can guess that the sun will not be there forever, but as long as we have been on this earth, we have seen the sunrise. Until we see evidence to the contrary, we must assume that it will happen until the end of time.
2. I also believe that the events within the bubble will be identical each time, assuming everything happens the exact same way each time. "Does each cause have a specific effect?" To an extent, yes. If we were to take a marble and bounce it off of another marble, the second will shoot off. If we were to repeat this experiment and made sure that the marble hits in the exact same place and is propelled at the exact same force, the second marble will react the same way. If we changed one thing, however, like putting a rock in the way, the second marble will react the same exact way UNTIL it comes into contact with a rock. This could lead into a discussion of time travel to affect future events.
3. If I were to punch someone in the face, it would elicit a reaction from them. That reaction would be defined by that individual's personal experiences. If this person was Gandhi, he would likely turn the other cheek. Some Irish drunkard, however, would almost certainly hit back. This little interaction may make it onto the news, depending on the severity of the ensuing brawl, and would therefore influence young viewers and affect whether a parent would adjust their style of parenting to accomodate the previously mentioned event.
This way, free will is preserved. No one event will completely dictate the actions of those involved. There is strong influence, yes, but many have had good parents and were taught good values who went on to do terrible things. The opposite is true as well. One cannot draw a correlation between good parenting and bad actions later in life.