I upgraded my java to 1.7.0_60, apparently it was old because I use chrome as by browser and it doesn't have a 64-bit version. It didn't fix the problem however. I still get the exactly same behaviour when closing down minecraft, even though the launcher clearly states that the java is upgraded.
As for two separate processes, I can only see one: http://goo.gl/7XKyns Maybe there is a difference between os-x and windows, but what I expect is that when selecting minecraft and clicking "end task" the whole program would terminate. But afterwards I still can hear game sounds and see this in the processes-tab in task manager: http://goo.gl/8f6z46 (sorry for the finnish ui)
Not totally similar, I was able to terminate the javaw.exe normally at any moment. It also only happened if I closed minecraft through task manager, not after normal exiting.
No, I had never even heard of it before searching just now. I don't see how it could have any effect in a single-player world though.
I believe I'm experiencing the same issue, managed to easily reproduce it in creative mode in a newly generated world:
https://www.youtube.com/watch?v=ldB0I16rzbo
You can see how the gateway spawns you inside the bedrock. In my case this lead to being looped between the gateways but I could also imagine it leading you to be pushed out into the void.