Has a deja vu really happened in an alternate lifetime?

I don't know all the facts, but I do believe in deja vu and quantum leaping, etc. It's wild when you think about it, but anything is possible, y'know?

No, no, and no. First, let's talk about quantum jumping. I assume you mean the idea that a person can some how 'jump' to an alternate quantum universe. (There is another type of quantum jumping, which actually does occur, where a system will jump between quantum states, but this is not related to what you are talking about.) Not only is there no evidence that quantum jumping is possible or occurs, the very notion of quantum jumping explicitly contradicts the notion of alternate universes. If one could freely move between two universes, the universes would not be separate universes. A universe, by definition, contains all things that can have an effect within it. This whole idea of quantum jumping is no more than wishful thinking and greed by those who want to sell you an idea that has zero validity.

Now, could there be alternate universes and thus, alternate lives? Well, sure, there could be. But if there were, we would have no way of knowing about it or interacting with it. That is to say it would make zero difference to us in this universe. So asking about the possibility of alternate universes is similar to asking 'if there were unicorns, would they like rainbows?' Since unicorns do not exist, the is no practical value in considering this question. If you fancy considering this question, there is no harm in considering it and you are free to do so if it entertains you. But there is no practical value because either way, it has no effect on reality.

Finally, is deja vu some sort of connection between us in this universe and us in a different universe? No. As stated earlier, that would defy the definition of a universe. On top of that, there are much better explanations for deja vu that do not require invoking some far fetched idea that has zero physical evidence. Deja vu is a misfiring of the brain. The brain is a wonderful device that performs all sorts of complex task in a truly amazing fashion. But, like any device, it occasionally has errors. Have you ever thought you saw something out of the corner of your eye and then looked at it more closely to find that it was something else entirely? Well, that is due to the way your brain parses images and occurs when an image is attributed to something that it is not, which is also a brain misfire of sorts. There is a part of the brain that triggers whenever something familiar happens, so that you know whether or not what you are experiencing is new or something you have experienced before. Sometimes that part of the brain misfires, giving you the feeling that you have experienced something previously, when you have, in fact, not. In people who have brain injuries, this function can be damaged leading to those people never feeling like they have experienced something before, or always feeling like they have.

All deja vu is is an accidental mistriggering of one of the millions of complex, sophisticated operations that occur constantly within the brain. You do not need to make up new universes and outrageous new laws of physics to explain it.