@glS I also feel the question is too massive. I should really edit it. I have gained clarity from our discussion. The question is as it currently framed it assumes the whole place is a mine field and tells you where there are suspected mines. But I now know there are far fewer mines. I'm waiting to for more clarity and then I'll edit the question :)

Thank you for this wonderful discussion and the effort!

@MoreAnonymous sure it is! questions/answers can be edited at any time, bounties don't really change anything

@MoreAnonymous to be honest, I also don't really understand why we should strive so much to come out with a "time-energy uncertainty relation". The way I see it, time is not an observable in QM, thus there is no uncertainty relation for it in the same sense that there is for pairs of observables

I guess it's nice that in some cases you can come out with something, but for example for the interpretation given by josh in that answer, that only works in some specific cases

if you ask me, the best way to relate "energy uncertainty" and "time" is to notice that the energy uncertainty is equal to the "velocity of evolution" in state space (where here "velocity" is essentially the "angular velocity" of pure states in the projective hilbert space), in a way that can be made very precise. You might want to look at quantum speed limits for this line of reasoning

@MoreAnonymous it's a bit too long yea. I mean I understand where you come from: people ask you for details and sources, and if you thought about the subject matter for a while you might have lots of it. And of course, often if you are asking the question you do not have a clear idea of what's important and what isn't, so you might end up adding lots of things that are not actually going to be useful. Asking good questions on stackexchange is much harder than giving good answers

but yea now that you hopefully have a clearer idea of what's what, it might be useful to remove some parts of the question to make it more streamlined.

@MoreAnonymous yes I'll edit it in later

@glS Oh thanks! Didn't know about that :)

@glS I think the reason you don't feel my pain is that I feel we have a variable $t'$ in the $\Delta E \Delta t'$ where $f(t) = t'$ but we don't know $f$

Which I find frustrating

@glS Oh enlightened one share you wisdom with a link :P

@glS At the point of time I asked the question I was so confused about the whole thing which is what led to the mine field.

@glS Does it have a nice (or intuitive) interpretation of time as well like josh's (when his works)?

@glS yes. I found it quite hard. I felt like the carpet beneath my feet had been pulled because one piece of the puzzle wasn't fitting and hence I questioned them all. I don't think I'll edit it now because it might seem to some as a gamification of the QC SE's edit option. Where I'll edit my question and you'll edit your answer.