Interconnected in a certain sense, sure. I can write this and you can read this.
No, interconnected in a physical sense. This is because of the "spooky action at a distance" thing and the fact that we were all linked in a single point as spooky action requires when the big bang happened. Another side note: telepathy was demonstrated scientifically with a 7% difference in results while used. It is little but anything over 0% is enough to prove.
Perception of self depends on specific function of the brain. Body and Brain will die...
You are an amalgam of matter and "mental stuff" like thoughts, emotions etc. Who is observing these thoughts, emotions, sensations etc. ? Nobody
There are multiple interpretations of QM. Tell me how I can observe 100 pounds of gold into existence.
It is quite an exact science and they were even able to built quantum computers. It is extraordinarily expensive to build them because not only if a human is observing the "spooky stuff" happening there it will stop working but also a lifeless electron in the wrong place observing that would make it stop function.
Of course it does not work like that, making 100pounds of gold by observing. That is not one of the implications but the other implications of quantum mechanics are super-shocking enough.
The problem, though, is that there's no karmic link and no continuity of consciousness among these different versions of "you". So although multiverse theory does imply a sort of rebirth, it's not the same as rebirth in Buddhism.
The brain that is linked with consciousness does not require an identical body to this human one we are having right now. It does also not require an identical shaped brain in order to give rise to the same consciousness. This consciousness could then be present in a hell-being. As somebody just pointed out buddha said consciousness gave rise to body and form not the other way around. We will never be able to prove or disprove any of these possibilities. If you consider this body gave rise to consciousness that is an asumption based on intuition also because this problem we are talking about is like string theory, impossible to prove or disprove. However intuitive, it is just intuitive and will forever remain imposible to prove.
I don't give too much pennies on things like this but maybe worth mentioning: There were long studies made about people calaiming to remember past lives. They used 3 to 1 girl-male ratio or ratios like this because it was likely they will remember been also female or male and all studies shown exact 50-50% female-male ratio and also respected the social ladder, thus rulling out the "napoleonian syndrome". Some even spoke unknown languages or arhaic, regional languages etc. but anyway this is not something to give to much pennies on but worth a mention.
Keep in mind budha said intelectual thinking would lead only to further confusion in the case of the 4 unthinkables and said never to belive anything not even if he said it and teached the method to find out for ourselves. That is the only thing we can do. Questioning is a very apreciated attitude in budhism because that is how it started in the first place and only through questionig you will find the answer. Science and other religions leave a thousain of questions unanswered or contradict itself. Budhism has no contradictions or logical flaws, just a couple of things that can never pe proven or unproven through intelectual thinking, like string theory. Using the path teached by it seems the only way to get through this dead-end.