Re: Imagine somehow you build a a time tunnel that stretches 1 minute into the past..
I don't see how that resolves the problem of any variation of the basic causality paradox: by going back in time and killing yourself, you have removed the reason to go back and kill yourself. Because you are dead, you do not go back in time and kill yourself. Because you do not go back in time and kill yourself, you are not dead, so you do go back in time and kill yourself.
Repeat cycle infinitely. (And/or, the universe breaks and a lot of people are upset)
Unless there is presently established physics that says what happens in this instance is something other than that - and I was fairly certain we're not anywhere close to that at this point - I don't see how the above isn't still a problem. You note that your/his solution results from "an idea of various Quantum Sciences theories on time lines (perhaps better said as time conditions", but what are they and have said theories been proven? I suspect the answer remains "we don't really know, but it's probably bad and it makes my brain hurt".
Look at is this way.
Going back in time to time to kill yourself is a misnomer. Who you are killing is a carbon copy of yourself, it is not like putting a gun to your own head. The whole idea here is going back through time one minute to a point before you yourself went through the device. The problem is in that instance there are two people standing there that are identical less one minute of their lives (the traveler has an additional minute.)
The act of going back in time is the important factor here to consider, then we need to evaluate the point of view of them both. What did they both really observe and what is the theoretical end result?
The one that went through we can call a traveler. What he observed was everything the other version of himself observed but with the additional step of going through the device (whatever that entails but is immaterial to this conversation) and ending up in the same room one minute prior. The traveler's timeline is still occurring for him, all of those things happened for him. The point that they are the same person is diminished in importance because of the condition, two people standing there in an instance of time that they both observe (sort of.)
The version of himself that has not gone through the device is interesting to consider. Technically all he observed is walking into a room with a time device, then all of a sudden they are dead. It might be important to theorize where the traveler ends up in the room but in many ways it does not change the outcome (assuming nothing messy happened but we can theorize the whole point is to not end up with two people trying to stand in the same exact space as the exact same point in their collective time.)
To go a step further, after the traveler kills the version of himself standing there, he can then destroy the device... and he is still standing there on his continued timeline after all of those events occurred for his timeline to that point. The timeline for the version dead is concluded, presumably the body is still on the floor in the same room.
What we do not have evidence of is some corrective action that time takes because of someone going back in time. What we have evidence of is that person who went through the device still subject to our physical laws once in our reality, less one minute that he traveled back in time. No one is necessarily frozen in time, and we can only theorize how everyone in the room would really act if they were facing one another.
The real paradox here is what happens if there is a third person in the room observing all of this.
Consider *that* point of view. One minute there is someone about to go through a time device, then that person goes through the device. By theory what happens next is instantaneous, that observer is all of a sudden seeing the same person with a gun and a carbon copy of that same person on the floor dead. But, what exactly did that observer really observe? Time is still occurring for everyone in the room by theory, so does the observer's reality "correct" to the concluded events as impacted by the traveler also standing there with a gun? We assume so. But if so, what happened to that observance of watching someone go through the device? Was it lost, and perhaps better asked... did it ever happen? Remember after all of this is concluded the observer is standing there, and so are two people that look identical with one of them being dead. Even a better question is did the observer end up on a new timeline? And with that question we get to also ask, is time really linear?
Now we get to have a headache, and off I go for more bourbon.